-
Vectors | Chapter 1, Essence of linear algebra
Beginning the linear algebra series with the basics.
Help fund future projects: https://www.patreon.com/3blue1brown
Correction: 6:52, the screen should show [x1, y1] + [x2, y2] = [x1+x2, y1+y2]
Music: https://vincerubinetti.bandcamp.com/track/grants-etude
Thanks to Elo Marie Viennot and Ambros Gleixner from HTW Berlin (www.htw-berlin.de) for contributing German translations and dubbing.
Thanks also to these viewers for their contributions to the subtitles
Arabic: @Cewkins, Hazem
Bengali: Md Rasheduzzaman
Czech: @Chnapak
Greek: Nikolaos Tsagkas
Hebrew: Omer Tuchfeld
Italian: mattiacolucci
Spanish: Juan Carlos Largo
Thai: own doggoV●ᴥ●V
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want ...
published: 06 Aug 2016
-
Linear Algebra - Full College Course
Learn Linear Algebra in this 20-hour college course. Watch the second half here: https://youtu.be/DJ6YwBN7Ya8
This course is taught by Dr. Jim Hefferon, a professor of mathematics at St Michael's College.
📔 The course follows along with Dr. Hefferon's Linear Algebra text book. The book is available for free: http://joshua.smcvt.edu/linearalgebra/book.pdf
📚 Access additional course resources at: https://hefferon.net/linearalgebra/
🔗 Stephen Chew's Learning How to Learn series: https://www.youtube.com/watch?v=htv6eap1-_M&list=PL85708E6EA236E3DB
🔗 3Blue1Brown's Linear Algebra series: https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
⭐️ Course Contents ⭐️
⌨️ (0:00:00) Introduction to Linear Algebra by Hefferon
⌨️ (0:04:35) One.I.1 Solving Linear Systems, P...
published: 19 Nov 2020
-
Essence of linear algebra preview
Home page: https://www.3blue1brown.com/
This introduces the "Essence of linear algebra" series, aimed at animating the geometric intuitions underlying many of the topics taught in a standard linear algebra course.
Error corrections:
- At one point I mistakenly allude to calculators using the Taylor expansion of sine for its computations, when in reality most use CORDIC (or something like it).
- Around 30 seconds in, there is a typo in how the determinant is written, which should be ad - bc
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And yo...
published: 05 Aug 2016
-
Gil Strang's Final 18.06 Linear Algebra Lecture
Speakers: Gilbert Strang, Alan Edelman, Pavel Grinfeld, Michel Goemans
Revered mathematics professor Gilbert Strang capped a 61-year career as a faculty member at MIT by delivering his final 18.06 Linear Algebra lecture before retiring at the age of 88. In addition to a brief review for the course final exam, the overflowing audience (both in person and on the live YouTube stream) heard recollections, appreciations, and congratulations from Prof. Strang’s colleagues and former students. A rousing standing ovation concluded this historic event.
0:00 - Seating
8:56 - Class start
10:05 - Alan Edelman's speech about Gilbert Strang
12:57 - Gilbert Strang's introduction
15:42 - Solving linear equations
30:42 - Visualization of four-dimensional space
31:37 - Nonzero Solutions
32:16 - Finding...
published: 15 May 2023
-
Gilbert Strang: Linear Algebra vs Calculus
Full episode with Gilbert Strang (Nov 2019): https://www.youtube.com/watch?v=lEZPfmGCEk0
New clips channel (Lex Clips): https://www.youtube.com/lexclips
Once it reaches 20,000 subscribers, I'll start posting the clips there instead.
(more links below)
For now, new full episodes are released once or twice a week and 1-2 new clips or a new non-podcast video is released on all other days.
Clip from full episode: https://www.youtube.com/watch?v=lEZPfmGCEk0 If you enjoy these clips, subscribe to the new clips channel (Lex Clips): https://www.youtube.com/lexclips Once it reaches 20,000 subscribers, I'll start posting the clips there instead. For now, new full episodes are released once or twice a week and 1-2 new clips or a new non-podcast video is released on all other days.
(more links belo...
published: 27 Nov 2019
-
Linear Algebra - Matrix Operations
A quick review of basic matrix operations.
published: 18 Aug 2020
-
Linear transformations and matrices | Chapter 3, Essence of linear algebra
Quite possibly the most important idea for understanding linear algebra.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Home page: https://www.3blue1brown.com
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Spanish: Juan Carlos Largo
Vietnamese: @ngvutuan2811
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell...
published: 07 Aug 2016
-
The Best Way To Learn Linear Algebra
My Courses: https://www.freemathvids.com/ || I discuss the best way to learn linear algebra and give you some options. Do you have advice for people? If so, please leave a comment below.
Proof Writing Book: https://amzn.to/3PTCdlz
Anton's Linear Algebra: https://amzn.to/48zsE2D
Another: https://amzn.to/48qhoFL
Yet another: https://amzn.to/3PS2jFA
Friedberg, Insel, Spence Linear Algebra: https://amzn.to/3PGUG3E
Useful Math Supplies https://amzn.to/3Y5TGcv
My Recording Gear https://amzn.to/3BFvcxp
(these are my affiliate links)
***********Math, Physics, and Computer Science Books***********
Epic Math Book List https://amzn.to/3F98vT1
Pre-algebra, Algebra, and Geometry https://amzn.to/3FdbwSn
College Algebra, Precalculus, and Trigonometry https://amzn.to/3UKjvfb
Probability and Statistics ht...
published: 07 Oct 2023
-
Geometry of Linear Algebra
MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Linan Chen
A teaching assistant works through a problem on the geometry of linear algebra.
Watch this in Chinese: https://youtu.be/mgbjhzDndOY
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
published: 25 Jul 2018
-
Intro to Matrices
This precalculus video tutorial provides a basic introduction into matrices. It covers matrix notation and how to determine the order of a matrix and the value of the elements inside a matrix. This video also covers the addition and subtraction of matrices as well as the scalar multiplication of matrices.
Matrices - Free Formula Sheet:
https://bit.ly/3UE9Cmk
_________________________________
Introduction to Matrices:
https://www.youtube.com/watch?v=yRwQ7A6jVLk
Adding and Subtracting Matrices:
https://www.youtube.com/watch?v=QXUbFzEd3Ww
Scalar Multiplication of Matrices:
https://www.youtube.com/watch?v=iJERwUVuwtY
Solving Matrix Equations:
https://www.youtube.com/wat...
published: 16 Feb 2018
9:52
Vectors | Chapter 1, Essence of linear algebra
Beginning the linear algebra series with the basics.
Help fund future projects: https://www.patreon.com/3blue1brown
Correction: 6:52, the screen should show [x...
Beginning the linear algebra series with the basics.
Help fund future projects: https://www.patreon.com/3blue1brown
Correction: 6:52, the screen should show [x1, y1] + [x2, y2] = [x1+x2, y1+y2]
Music: https://vincerubinetti.bandcamp.com/track/grants-etude
Thanks to Elo Marie Viennot and Ambros Gleixner from HTW Berlin (www.htw-berlin.de) for contributing German translations and dubbing.
Thanks also to these viewers for their contributions to the subtitles
Arabic: @Cewkins, Hazem
Bengali: Md Rasheduzzaman
Czech: @Chnapak
Greek: Nikolaos Tsagkas
Hebrew: Omer Tuchfeld
Italian: mattiacolucci
Spanish: Juan Carlos Largo
Thai: own doggoV●ᴥ●V
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
https://wn.com/Vectors_|_Chapter_1,_Essence_Of_Linear_Algebra
Beginning the linear algebra series with the basics.
Help fund future projects: https://www.patreon.com/3blue1brown
Correction: 6:52, the screen should show [x1, y1] + [x2, y2] = [x1+x2, y1+y2]
Music: https://vincerubinetti.bandcamp.com/track/grants-etude
Thanks to Elo Marie Viennot and Ambros Gleixner from HTW Berlin (www.htw-berlin.de) for contributing German translations and dubbing.
Thanks also to these viewers for their contributions to the subtitles
Arabic: @Cewkins, Hazem
Bengali: Md Rasheduzzaman
Czech: @Chnapak
Greek: Nikolaos Tsagkas
Hebrew: Omer Tuchfeld
Italian: mattiacolucci
Spanish: Juan Carlos Largo
Thai: own doggoV●ᴥ●V
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
- published: 06 Aug 2016
- views: 8973546
11:39:45
Linear Algebra - Full College Course
Learn Linear Algebra in this 20-hour college course. Watch the second half here: https://youtu.be/DJ6YwBN7Ya8
This course is taught by Dr. Jim Hefferon, a profe...
Learn Linear Algebra in this 20-hour college course. Watch the second half here: https://youtu.be/DJ6YwBN7Ya8
This course is taught by Dr. Jim Hefferon, a professor of mathematics at St Michael's College.
📔 The course follows along with Dr. Hefferon's Linear Algebra text book. The book is available for free: http://joshua.smcvt.edu/linearalgebra/book.pdf
📚 Access additional course resources at: https://hefferon.net/linearalgebra/
🔗 Stephen Chew's Learning How to Learn series: https://www.youtube.com/watch?v=htv6eap1-_M&list=PL85708E6EA236E3DB
🔗 3Blue1Brown's Linear Algebra series: https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
⭐️ Course Contents ⭐️
⌨️ (0:00:00) Introduction to Linear Algebra by Hefferon
⌨️ (0:04:35) One.I.1 Solving Linear Systems, Part One
⌨️ (0:26:08) One.I.1 Solving Linear Systems, Part Two
⌨️ (0:40:56) One.I.2 Describing Solution Sets, Part One
⌨️ (0:54:21) One.I.2 Describing Solution Sets, Part Two
⌨️ (1:02:48) One.I.3 General = Particular + Homogeneous
⌨️ (1:18:33) One.II.1 Vectors in Space
⌨️ (1:35:08) One.II.2 Vector Length and Angle Measure
⌨️ (1:51:31) One.III.1 Gauss-Jordan Elimination
⌨️ (2:00:00) One.III.2 The Linear Combination Lemma
⌨️ (2:44:32) Two.I.1 Vector Spaces, Part One
⌨️ (3:08:12) Two.I.1 Vector Spaces, Part Two
⌨️ (3:33:01) Two.I.2 Subspaces, Part One
⌨️ (3:58:16) Two.I.2 Subspaces, Part Two
⌨️ (4:23:43) Two.II.1 Linear Independence, Part One
⌨️ (4:45:11) Two.II.1 Linear Independence, Part Two
⌨️ (5:03:57) Two.III.1 Basis, Part One
⌨️ (5:23:55) Two.III.1 Basis, Part Two
⌨️ (5:42:34) Two.III.2 Dimension
⌨️ (6:03:24) Two.III.3 Vector Spaces and Linear Systems
⌨️ (6:25:09) Three.I.1 Isomorphism, Part One
⌨️ (6:54:08) Three.I.1 Isomorphism, Part Two
⌨️ (7:21:47) Three.I.2 Dimension Characterizes Isomorphism
⌨️ (7:43:43) Three.II.1 Homomorphism, Part One
⌨️ (8:14:52) Three.II.1 Homomorphism, Part Two
⌨️ (8:30:24) Three.II.2 Range Space and Null Space, Part One
⌨️ (9:00:17) Three.II.2 Range Space and Null Space, Part Two.
⌨️ (9:20:57) Three.II Extra Transformations of the Plane
⌨️ (9:52:06) Three.III.1 Representing Linear Maps, Part One.
⌨️ (10:13:18) Three.III.1 Representing Linear Maps, Part Two
⌨️ (10:34:18) Three.III.2 Any Matrix Represents a Linear Map
⌨️ (10:58:32) Three.IV.1 Sums and Scalar Products of Matrices
⌨️ (11:19:14) Three.IV.2 Matrix Multiplication, Part One
⌨️ Three.IV.2 Matrix Multiplication, Part Two (We accidentally left this section out. Watch it here: https://youtu.be/aWubyx5bBn4)
The following sections are in the second video: https://youtu.be/DJ6YwBN7Ya8
⌨️ Three.IV.3 Mechanics of Matrix Multiplication
⌨️ Three.IV.4 Matrix Inverse, Part One
⌨️ Three.IV.4 Matrix Inverse, Part Two
⌨️ Three.V.1 Changing Vector Representations
⌨️ Three.V.2 Changing Map Representations, Part One
⌨️ Three.V.2 Changing Map Representations, Part Two
⌨️ Three.VI Projection
⌨️ Four.I.1 Determinants
⌨️ Four.I.3 Permutation Expansion, Part One
⌨️ Four.I.3 Permutation Expansion, Part Two
⌨️ Four.I.4 Determinants Exist (optional)
⌨️ Four.II.1 Geometry of Determinants
⌨️ Four.III.1 Laplace's formula for the determinant
⌨️ Five.I.1 Complex Vector Spaces
⌨️ Five.II.1 Similarity
⌨️ Five.II.2 Diagonalizability
⌨️ Five.II.3 Eigenvalues and Eigenvectors, Part One
⌨️ Five.II.3 Eigenvalues and Eigenvectors, Part Two
⌨️ Five.II.3 Geometry of Eigenvalues and Eigenvectors
--
Learn to code for free and get a developer job: https://www.freecodecamp.org
Read hundreds of articles on programming: https://freecodecamp.org/news
https://wn.com/Linear_Algebra_Full_College_Course
Learn Linear Algebra in this 20-hour college course. Watch the second half here: https://youtu.be/DJ6YwBN7Ya8
This course is taught by Dr. Jim Hefferon, a professor of mathematics at St Michael's College.
📔 The course follows along with Dr. Hefferon's Linear Algebra text book. The book is available for free: http://joshua.smcvt.edu/linearalgebra/book.pdf
📚 Access additional course resources at: https://hefferon.net/linearalgebra/
🔗 Stephen Chew's Learning How to Learn series: https://www.youtube.com/watch?v=htv6eap1-_M&list=PL85708E6EA236E3DB
🔗 3Blue1Brown's Linear Algebra series: https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
⭐️ Course Contents ⭐️
⌨️ (0:00:00) Introduction to Linear Algebra by Hefferon
⌨️ (0:04:35) One.I.1 Solving Linear Systems, Part One
⌨️ (0:26:08) One.I.1 Solving Linear Systems, Part Two
⌨️ (0:40:56) One.I.2 Describing Solution Sets, Part One
⌨️ (0:54:21) One.I.2 Describing Solution Sets, Part Two
⌨️ (1:02:48) One.I.3 General = Particular + Homogeneous
⌨️ (1:18:33) One.II.1 Vectors in Space
⌨️ (1:35:08) One.II.2 Vector Length and Angle Measure
⌨️ (1:51:31) One.III.1 Gauss-Jordan Elimination
⌨️ (2:00:00) One.III.2 The Linear Combination Lemma
⌨️ (2:44:32) Two.I.1 Vector Spaces, Part One
⌨️ (3:08:12) Two.I.1 Vector Spaces, Part Two
⌨️ (3:33:01) Two.I.2 Subspaces, Part One
⌨️ (3:58:16) Two.I.2 Subspaces, Part Two
⌨️ (4:23:43) Two.II.1 Linear Independence, Part One
⌨️ (4:45:11) Two.II.1 Linear Independence, Part Two
⌨️ (5:03:57) Two.III.1 Basis, Part One
⌨️ (5:23:55) Two.III.1 Basis, Part Two
⌨️ (5:42:34) Two.III.2 Dimension
⌨️ (6:03:24) Two.III.3 Vector Spaces and Linear Systems
⌨️ (6:25:09) Three.I.1 Isomorphism, Part One
⌨️ (6:54:08) Three.I.1 Isomorphism, Part Two
⌨️ (7:21:47) Three.I.2 Dimension Characterizes Isomorphism
⌨️ (7:43:43) Three.II.1 Homomorphism, Part One
⌨️ (8:14:52) Three.II.1 Homomorphism, Part Two
⌨️ (8:30:24) Three.II.2 Range Space and Null Space, Part One
⌨️ (9:00:17) Three.II.2 Range Space and Null Space, Part Two.
⌨️ (9:20:57) Three.II Extra Transformations of the Plane
⌨️ (9:52:06) Three.III.1 Representing Linear Maps, Part One.
⌨️ (10:13:18) Three.III.1 Representing Linear Maps, Part Two
⌨️ (10:34:18) Three.III.2 Any Matrix Represents a Linear Map
⌨️ (10:58:32) Three.IV.1 Sums and Scalar Products of Matrices
⌨️ (11:19:14) Three.IV.2 Matrix Multiplication, Part One
⌨️ Three.IV.2 Matrix Multiplication, Part Two (We accidentally left this section out. Watch it here: https://youtu.be/aWubyx5bBn4)
The following sections are in the second video: https://youtu.be/DJ6YwBN7Ya8
⌨️ Three.IV.3 Mechanics of Matrix Multiplication
⌨️ Three.IV.4 Matrix Inverse, Part One
⌨️ Three.IV.4 Matrix Inverse, Part Two
⌨️ Three.V.1 Changing Vector Representations
⌨️ Three.V.2 Changing Map Representations, Part One
⌨️ Three.V.2 Changing Map Representations, Part Two
⌨️ Three.VI Projection
⌨️ Four.I.1 Determinants
⌨️ Four.I.3 Permutation Expansion, Part One
⌨️ Four.I.3 Permutation Expansion, Part Two
⌨️ Four.I.4 Determinants Exist (optional)
⌨️ Four.II.1 Geometry of Determinants
⌨️ Four.III.1 Laplace's formula for the determinant
⌨️ Five.I.1 Complex Vector Spaces
⌨️ Five.II.1 Similarity
⌨️ Five.II.2 Diagonalizability
⌨️ Five.II.3 Eigenvalues and Eigenvectors, Part One
⌨️ Five.II.3 Eigenvalues and Eigenvectors, Part Two
⌨️ Five.II.3 Geometry of Eigenvalues and Eigenvectors
--
Learn to code for free and get a developer job: https://www.freecodecamp.org
Read hundreds of articles on programming: https://freecodecamp.org/news
- published: 19 Nov 2020
- views: 2058280
5:09
Essence of linear algebra preview
Home page: https://www.3blue1brown.com/
This introduces the "Essence of linear algebra" series, aimed at animating the geometric intuitions underlying many of t...
Home page: https://www.3blue1brown.com/
This introduces the "Essence of linear algebra" series, aimed at animating the geometric intuitions underlying many of the topics taught in a standard linear algebra course.
Error corrections:
- At one point I mistakenly allude to calculators using the Taylor expansion of sine for its computations, when in reality most use CORDIC (or something like it).
- Around 30 seconds in, there is a typo in how the determinant is written, which should be ad - bc
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
https://wn.com/Essence_Of_Linear_Algebra_Preview
Home page: https://www.3blue1brown.com/
This introduces the "Essence of linear algebra" series, aimed at animating the geometric intuitions underlying many of the topics taught in a standard linear algebra course.
Error corrections:
- At one point I mistakenly allude to calculators using the Taylor expansion of sine for its computations, when in reality most use CORDIC (or something like it).
- Around 30 seconds in, there is a typo in how the determinant is written, which should be ad - bc
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
- published: 05 Aug 2016
- views: 2329876
1:05:09
Gil Strang's Final 18.06 Linear Algebra Lecture
Speakers: Gilbert Strang, Alan Edelman, Pavel Grinfeld, Michel Goemans
Revered mathematics professor Gilbert Strang capped a 61-year career as a faculty memb...
Speakers: Gilbert Strang, Alan Edelman, Pavel Grinfeld, Michel Goemans
Revered mathematics professor Gilbert Strang capped a 61-year career as a faculty member at MIT by delivering his final 18.06 Linear Algebra lecture before retiring at the age of 88. In addition to a brief review for the course final exam, the overflowing audience (both in person and on the live YouTube stream) heard recollections, appreciations, and congratulations from Prof. Strang’s colleagues and former students. A rousing standing ovation concluded this historic event.
0:00 - Seating
8:56 - Class start
10:05 - Alan Edelman's speech about Gilbert Strang
12:57 - Gilbert Strang's introduction
15:42 - Solving linear equations
30:42 - Visualization of four-dimensional space
31:37 - Nonzero Solutions
32:16 - Finding Solutions
34:19 - Elimination Process
41:05 - Introduction to Equations
42:26 - Finding Solutions
44:29 - Solution 1
47:42 - Rank of the Matrix
51:39 - In appreciation of Gilbert Strang
52:08 - Congratulations on retirement
52:38 - Personal experiences with Strang
55:01 - Life lessons learned from Strang
1:01:08 - Gil Strang's impact on math education
1:01:44 - Gil Strang's teaching style
1:02:20 - Gil Strang's legacy
1:03:23 - Congratulations to Gil Strang
This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu.
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
Support OCW at http://ow.ly/a1If50zVRlQ
We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.
https://wn.com/Gil_Strang's_Final_18.06_Linear_Algebra_Lecture
Speakers: Gilbert Strang, Alan Edelman, Pavel Grinfeld, Michel Goemans
Revered mathematics professor Gilbert Strang capped a 61-year career as a faculty member at MIT by delivering his final 18.06 Linear Algebra lecture before retiring at the age of 88. In addition to a brief review for the course final exam, the overflowing audience (both in person and on the live YouTube stream) heard recollections, appreciations, and congratulations from Prof. Strang’s colleagues and former students. A rousing standing ovation concluded this historic event.
0:00 - Seating
8:56 - Class start
10:05 - Alan Edelman's speech about Gilbert Strang
12:57 - Gilbert Strang's introduction
15:42 - Solving linear equations
30:42 - Visualization of four-dimensional space
31:37 - Nonzero Solutions
32:16 - Finding Solutions
34:19 - Elimination Process
41:05 - Introduction to Equations
42:26 - Finding Solutions
44:29 - Solution 1
47:42 - Rank of the Matrix
51:39 - In appreciation of Gilbert Strang
52:08 - Congratulations on retirement
52:38 - Personal experiences with Strang
55:01 - Life lessons learned from Strang
1:01:08 - Gil Strang's impact on math education
1:01:44 - Gil Strang's teaching style
1:02:20 - Gil Strang's legacy
1:03:23 - Congratulations to Gil Strang
This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu.
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- published: 15 May 2023
- views: 2501087
2:14
Gilbert Strang: Linear Algebra vs Calculus
Full episode with Gilbert Strang (Nov 2019): https://www.youtube.com/watch?v=lEZPfmGCEk0
New clips channel (Lex Clips): https://www.youtube.com/lexclips
Once it...
Full episode with Gilbert Strang (Nov 2019): https://www.youtube.com/watch?v=lEZPfmGCEk0
New clips channel (Lex Clips): https://www.youtube.com/lexclips
Once it reaches 20,000 subscribers, I'll start posting the clips there instead.
(more links below)
For now, new full episodes are released once or twice a week and 1-2 new clips or a new non-podcast video is released on all other days.
Clip from full episode: https://www.youtube.com/watch?v=lEZPfmGCEk0 If you enjoy these clips, subscribe to the new clips channel (Lex Clips): https://www.youtube.com/lexclips Once it reaches 20,000 subscribers, I'll start posting the clips there instead. For now, new full episodes are released once or twice a week and 1-2 new clips or a new non-podcast video is released on all other days.
(more links below)
Podcast full episodes playlist:
https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4
Podcasts clips playlist:
https://www.youtube.com/playlist?list=PLrAXtmErZgOeciFP3CBCIEElOJeitOr41
Podcast website:
https://lexfridman.com/ai
Podcast on Apple Podcasts (iTunes):
https://apple.co/2lwqZIr
Podcast on Spotify:
https://spoti.fi/2nEwCF8
Podcast RSS:
https://lexfridman.com/category/ai/feed/
Gilbert Strang is a professor of mathematics at MIT and perhaps one of the most famous and impactful teachers of math in the world. His MIT OpenCourseWare lectures on linear algebra have been viewed millions of times.
Subscribe to this YouTube channel or connect on:
- Twitter: https://twitter.com/lexfridman
- LinkedIn: https://www.linkedin.com/in/lexfridman
- Facebook: https://www.facebook.com/lexfridman
- Instagram: https://www.instagram.com/lexfridman
- Medium: https://medium.com/@lexfridman
- Support on Patreon: https://www.patreon.com/lexfridman
https://wn.com/Gilbert_Strang_Linear_Algebra_Vs_Calculus
Full episode with Gilbert Strang (Nov 2019): https://www.youtube.com/watch?v=lEZPfmGCEk0
New clips channel (Lex Clips): https://www.youtube.com/lexclips
Once it reaches 20,000 subscribers, I'll start posting the clips there instead.
(more links below)
For now, new full episodes are released once or twice a week and 1-2 new clips or a new non-podcast video is released on all other days.
Clip from full episode: https://www.youtube.com/watch?v=lEZPfmGCEk0 If you enjoy these clips, subscribe to the new clips channel (Lex Clips): https://www.youtube.com/lexclips Once it reaches 20,000 subscribers, I'll start posting the clips there instead. For now, new full episodes are released once or twice a week and 1-2 new clips or a new non-podcast video is released on all other days.
(more links below)
Podcast full episodes playlist:
https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4
Podcasts clips playlist:
https://www.youtube.com/playlist?list=PLrAXtmErZgOeciFP3CBCIEElOJeitOr41
Podcast website:
https://lexfridman.com/ai
Podcast on Apple Podcasts (iTunes):
https://apple.co/2lwqZIr
Podcast on Spotify:
https://spoti.fi/2nEwCF8
Podcast RSS:
https://lexfridman.com/category/ai/feed/
Gilbert Strang is a professor of mathematics at MIT and perhaps one of the most famous and impactful teachers of math in the world. His MIT OpenCourseWare lectures on linear algebra have been viewed millions of times.
Subscribe to this YouTube channel or connect on:
- Twitter: https://twitter.com/lexfridman
- LinkedIn: https://www.linkedin.com/in/lexfridman
- Facebook: https://www.facebook.com/lexfridman
- Instagram: https://www.instagram.com/lexfridman
- Medium: https://medium.com/@lexfridman
- Support on Patreon: https://www.patreon.com/lexfridman
- published: 27 Nov 2019
- views: 413795
10:59
Linear transformations and matrices | Chapter 3, Essence of linear algebra
Quite possibly the most important idea for understanding linear algebra.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form...
Quite possibly the most important idea for understanding linear algebra.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Home page: https://www.3blue1brown.com
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Spanish: Juan Carlos Largo
Vietnamese: @ngvutuan2811
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
https://wn.com/Linear_Transformations_And_Matrices_|_Chapter_3,_Essence_Of_Linear_Algebra
Quite possibly the most important idea for understanding linear algebra.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Home page: https://www.3blue1brown.com
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Spanish: Juan Carlos Largo
Vietnamese: @ngvutuan2811
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
- published: 07 Aug 2016
- views: 5302614
10:32
The Best Way To Learn Linear Algebra
My Courses: https://www.freemathvids.com/ || I discuss the best way to learn linear algebra and give you some options. Do you have advice for people? If so, ple...
My Courses: https://www.freemathvids.com/ || I discuss the best way to learn linear algebra and give you some options. Do you have advice for people? If so, please leave a comment below.
Proof Writing Book: https://amzn.to/3PTCdlz
Anton's Linear Algebra: https://amzn.to/48zsE2D
Another: https://amzn.to/48qhoFL
Yet another: https://amzn.to/3PS2jFA
Friedberg, Insel, Spence Linear Algebra: https://amzn.to/3PGUG3E
Useful Math Supplies https://amzn.to/3Y5TGcv
My Recording Gear https://amzn.to/3BFvcxp
(these are my affiliate links)
***********Math, Physics, and Computer Science Books***********
Epic Math Book List https://amzn.to/3F98vT1
Pre-algebra, Algebra, and Geometry https://amzn.to/3FdbwSn
College Algebra, Precalculus, and Trigonometry https://amzn.to/3UKjvfb
Probability and Statistics https://amzn.to/3FaaxCq
Discrete Mathematics https://amzn.to/3P6jPE4
Proof Writing https://amzn.to/3XXukxo
Calculus https://amzn.to/3iEH3F3
Differential Equations Books https://amzn.to/3Fac5wi
Partial Differential Equations Books https://amzn.to/3uyk1SV
Linear Algebra https://amzn.to/3VHiN3G
Abstract Algebra Books https://amzn.to/3FzLZEr
Real Analysis/Advanced Calculus https://amzn.to/3VIO4Ua
Complex Analysis https://amzn.to/3P6kbuo
Number Theory https://amzn.to/3UEm3vw
Graph Theory https://amzn.to/3BfRd5m
Topology https://amzn.to/3BiAGhe
Graduate Level Books https://amzn.to/3uv1eIg
Computer Science https://amzn.to/3Hh8kaU
Physics https://amzn.to/3BhPCMp
These are my affiliate links. As an Amazon Associate I earn from qualifying purchases.
If you enjoyed this video please consider liking, sharing, and subscribing.
Udemy Courses Via My Website: https://mathsorcerer.com
My FaceBook Page: https://www.facebook.com/themathsorcerer
My Instagram: https://www.instagram.com/therealmathsorcerer/
My TikTok: https://www.tiktok.com/@therealmathsorcerer
There are several ways that you can help support my channel:)
Consider becoming a member of the channel: https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join
My GoFundMe Page: https://www.gofundme.com/f/support-math-education-for-the-world
My Patreon Page: https://www.patreon.com/themathsorcerer
Donate via PayPal: https://paypal.com/donate/?cmd=_s-xclick&hosted_button_id=7XNKUGJUENSYU
************Udemy Courses(Please Use These Links If You Sign Up!)*************
Abstract Algebra Course
https://www.udemy.com/course/abstract-algebra-group-theory-with-the-math-sorcerer/?referralCode=B04607DA7A7D0E29272A
Advanced Calculus Course
https://www.udemy.com/course/advanced-calculusreal-analysis-with-the-math-sorcerer/?referralCode=0ABDD66D061D976EE232
Calculus 1 Course
https://www.udemy.com/course/calculus-1-with-the-math-sorcerer/?referralCode=E853B70ED36571CA9768
Calculus 2 Course
https://www.udemy.com/course/calculus-2-with-the-math-sorcerer/?referralCode=BAA5520B32FEA9827D54
Calculus 3 Course
https://www.udemy.com/course/calculus-3-with-the-math-sorcerer/?referralCode=296462D1897904C4BEB3
Calculus 1 Lectures with Assignments and a Final Exam
https://www.udemy.com/course/calculus-1-lectures-with-the-math-sorcerer/?referralCode=5D425153B63A8F506E30
Calculus Integration Insanity
https://www.udemy.com/course/calculus-integration-insanity-with-the-math-sorcerer/?referralCode=D533EEE31F90EDDAFF93
Differential Equations Course
https://www.udemy.com/course/differential-equations-with-the-math-sorcerer/?referralCode=4F0D91B41F7DACF4EC28
Differential Equations Lectures Course (Includes Assignments + Final Exam)
https://www.udemy.com/course/differential-equations-lectures-with-the-math-sorcerer/?referralCode=89E6CCC307A7A8627CD6
College Algebra Course
https://www.udemy.com/course/college-algebra-with-the-math-sorcerer/?referralCode=B2929EE97EF68DB9B69F
How to Write Proofs with Sets Course
https://www.udemy.com/course/how-to-write-proofs-in-set-theory-with-the-math-sorcerer/?referralCode=D503A7E3FB6916CF2D27
How to Write Proofs with Functions Course
https://www.udemy.com/course/how-to-write-proofs-with-functions-with-the-math-sorcerer/?referralCode=DBACD59AB7B16D4707CD
Trigonometry 1 Course
https://www.udemy.com/course/trigonometry-1-with-the-math-sorcerer/?referralCode=79E02DDFD4106A909AF5
Trigonometry 2 Course
https://www.udemy.com/course/trigonometry-2-with-the-math-sorcerer/?referralCode=7966E40F319B4FEF6535
Statistics with StatCrunch Course
https://www.udemy.com/course/statistics-with-statcrunch-by-the-math-sorcerer/?referralCode=69B27AF43D10924FF63B
Math Graduate Programs, Applying, Advice, Motivation
https://www.udemy.com/course/math-graduate-programs-applying-advice-motivation/?referralCode=70A1CED973D7910E9161
Daily Devotionals for Motivation with The Math Sorcerer
https://www.udemy.com/course/daily-math-devotionals-for-motivation-with-the-math-sorcerer/?referralCode=2653144E315A37A94B8C
Thank you:)
https://wn.com/The_Best_Way_To_Learn_Linear_Algebra
My Courses: https://www.freemathvids.com/ || I discuss the best way to learn linear algebra and give you some options. Do you have advice for people? If so, please leave a comment below.
Proof Writing Book: https://amzn.to/3PTCdlz
Anton's Linear Algebra: https://amzn.to/48zsE2D
Another: https://amzn.to/48qhoFL
Yet another: https://amzn.to/3PS2jFA
Friedberg, Insel, Spence Linear Algebra: https://amzn.to/3PGUG3E
Useful Math Supplies https://amzn.to/3Y5TGcv
My Recording Gear https://amzn.to/3BFvcxp
(these are my affiliate links)
***********Math, Physics, and Computer Science Books***********
Epic Math Book List https://amzn.to/3F98vT1
Pre-algebra, Algebra, and Geometry https://amzn.to/3FdbwSn
College Algebra, Precalculus, and Trigonometry https://amzn.to/3UKjvfb
Probability and Statistics https://amzn.to/3FaaxCq
Discrete Mathematics https://amzn.to/3P6jPE4
Proof Writing https://amzn.to/3XXukxo
Calculus https://amzn.to/3iEH3F3
Differential Equations Books https://amzn.to/3Fac5wi
Partial Differential Equations Books https://amzn.to/3uyk1SV
Linear Algebra https://amzn.to/3VHiN3G
Abstract Algebra Books https://amzn.to/3FzLZEr
Real Analysis/Advanced Calculus https://amzn.to/3VIO4Ua
Complex Analysis https://amzn.to/3P6kbuo
Number Theory https://amzn.to/3UEm3vw
Graph Theory https://amzn.to/3BfRd5m
Topology https://amzn.to/3BiAGhe
Graduate Level Books https://amzn.to/3uv1eIg
Computer Science https://amzn.to/3Hh8kaU
Physics https://amzn.to/3BhPCMp
These are my affiliate links. As an Amazon Associate I earn from qualifying purchases.
If you enjoyed this video please consider liking, sharing, and subscribing.
Udemy Courses Via My Website: https://mathsorcerer.com
My FaceBook Page: https://www.facebook.com/themathsorcerer
My Instagram: https://www.instagram.com/therealmathsorcerer/
My TikTok: https://www.tiktok.com/@therealmathsorcerer
There are several ways that you can help support my channel:)
Consider becoming a member of the channel: https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join
My GoFundMe Page: https://www.gofundme.com/f/support-math-education-for-the-world
My Patreon Page: https://www.patreon.com/themathsorcerer
Donate via PayPal: https://paypal.com/donate/?cmd=_s-xclick&hosted_button_id=7XNKUGJUENSYU
************Udemy Courses(Please Use These Links If You Sign Up!)*************
Abstract Algebra Course
https://www.udemy.com/course/abstract-algebra-group-theory-with-the-math-sorcerer/?referralCode=B04607DA7A7D0E29272A
Advanced Calculus Course
https://www.udemy.com/course/advanced-calculusreal-analysis-with-the-math-sorcerer/?referralCode=0ABDD66D061D976EE232
Calculus 1 Course
https://www.udemy.com/course/calculus-1-with-the-math-sorcerer/?referralCode=E853B70ED36571CA9768
Calculus 2 Course
https://www.udemy.com/course/calculus-2-with-the-math-sorcerer/?referralCode=BAA5520B32FEA9827D54
Calculus 3 Course
https://www.udemy.com/course/calculus-3-with-the-math-sorcerer/?referralCode=296462D1897904C4BEB3
Calculus 1 Lectures with Assignments and a Final Exam
https://www.udemy.com/course/calculus-1-lectures-with-the-math-sorcerer/?referralCode=5D425153B63A8F506E30
Calculus Integration Insanity
https://www.udemy.com/course/calculus-integration-insanity-with-the-math-sorcerer/?referralCode=D533EEE31F90EDDAFF93
Differential Equations Course
https://www.udemy.com/course/differential-equations-with-the-math-sorcerer/?referralCode=4F0D91B41F7DACF4EC28
Differential Equations Lectures Course (Includes Assignments + Final Exam)
https://www.udemy.com/course/differential-equations-lectures-with-the-math-sorcerer/?referralCode=89E6CCC307A7A8627CD6
College Algebra Course
https://www.udemy.com/course/college-algebra-with-the-math-sorcerer/?referralCode=B2929EE97EF68DB9B69F
How to Write Proofs with Sets Course
https://www.udemy.com/course/how-to-write-proofs-in-set-theory-with-the-math-sorcerer/?referralCode=D503A7E3FB6916CF2D27
How to Write Proofs with Functions Course
https://www.udemy.com/course/how-to-write-proofs-with-functions-with-the-math-sorcerer/?referralCode=DBACD59AB7B16D4707CD
Trigonometry 1 Course
https://www.udemy.com/course/trigonometry-1-with-the-math-sorcerer/?referralCode=79E02DDFD4106A909AF5
Trigonometry 2 Course
https://www.udemy.com/course/trigonometry-2-with-the-math-sorcerer/?referralCode=7966E40F319B4FEF6535
Statistics with StatCrunch Course
https://www.udemy.com/course/statistics-with-statcrunch-by-the-math-sorcerer/?referralCode=69B27AF43D10924FF63B
Math Graduate Programs, Applying, Advice, Motivation
https://www.udemy.com/course/math-graduate-programs-applying-advice-motivation/?referralCode=70A1CED973D7910E9161
Daily Devotionals for Motivation with The Math Sorcerer
https://www.udemy.com/course/daily-math-devotionals-for-motivation-with-the-math-sorcerer/?referralCode=2653144E315A37A94B8C
Thank you:)
- published: 07 Oct 2023
- views: 44546
16:36
Geometry of Linear Algebra
MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Linan Chen
A teaching assistant works through a prob...
MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Linan Chen
A teaching assistant works through a problem on the geometry of linear algebra.
Watch this in Chinese: https://youtu.be/mgbjhzDndOY
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
https://wn.com/Geometry_Of_Linear_Algebra
MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: https://ocw.mit.edu/18-06SCF11
Instructor: Linan Chen
A teaching assistant works through a problem on the geometry of linear algebra.
Watch this in Chinese: https://youtu.be/mgbjhzDndOY
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
- published: 25 Jul 2018
- views: 155390
11:23
Intro to Matrices
This precalculus video tutorial provides a basic introduction into matrices. It covers matrix notation and how to determine the order of a matrix and the value...
This precalculus video tutorial provides a basic introduction into matrices. It covers matrix notation and how to determine the order of a matrix and the value of the elements inside a matrix. This video also covers the addition and subtraction of matrices as well as the scalar multiplication of matrices.
Matrices - Free Formula Sheet:
https://bit.ly/3UE9Cmk
_________________________________
Introduction to Matrices:
https://www.youtube.com/watch?v=yRwQ7A6jVLk
Adding and Subtracting Matrices:
https://www.youtube.com/watch?v=QXUbFzEd3Ww
Scalar Multiplication of Matrices:
https://www.youtube.com/watch?v=iJERwUVuwtY
Solving Matrix Equations:
https://www.youtube.com/watch?v=UHhvcj0doaA
Multiplying Matrices:
https://www.youtube.com/watch?v=vzt9c7iWPxs
__________________________________
Gaussian Elimination & Row Echelon Form:
https://www.youtube.com/watch?v=eDb6iugi6Uk
Gauss Jordan Elimination:
https://www.youtube.com/watch?v=eYSASx8_nyg
Gaussian Elimination With 4 Variables:
https://www.youtube.com/watch?v=4VAXv6yRULU
Inverse of a 2x2 Matrix:
https://www.youtube.com/watch?v=aiBgjz5xbyg
Inverse of a 3x3 Matrix:
https://www.youtube.com/watch?v=Fg7_mv3izR0
__________________________________
Determinant of 2x2 and 3x3 Matrix:
https://www.youtube.com/watch?v=3ROzG6n4yMc
Determinant of 4x4 Matrix:
https://www.youtube.com/watch?v=fWzUwrt1Z0s
Cramer's Rule - 2x2 Linear System:
https://www.youtube.com/watch?v=vXqlIOX2itM
Cramer's Rule - 3x3 Linear System:
https://www.youtube.com/watch?v=Ot87qLTODdQ
___________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
https://wn.com/Intro_To_Matrices
This precalculus video tutorial provides a basic introduction into matrices. It covers matrix notation and how to determine the order of a matrix and the value of the elements inside a matrix. This video also covers the addition and subtraction of matrices as well as the scalar multiplication of matrices.
Matrices - Free Formula Sheet:
https://bit.ly/3UE9Cmk
_________________________________
Introduction to Matrices:
https://www.youtube.com/watch?v=yRwQ7A6jVLk
Adding and Subtracting Matrices:
https://www.youtube.com/watch?v=QXUbFzEd3Ww
Scalar Multiplication of Matrices:
https://www.youtube.com/watch?v=iJERwUVuwtY
Solving Matrix Equations:
https://www.youtube.com/watch?v=UHhvcj0doaA
Multiplying Matrices:
https://www.youtube.com/watch?v=vzt9c7iWPxs
__________________________________
Gaussian Elimination & Row Echelon Form:
https://www.youtube.com/watch?v=eDb6iugi6Uk
Gauss Jordan Elimination:
https://www.youtube.com/watch?v=eYSASx8_nyg
Gaussian Elimination With 4 Variables:
https://www.youtube.com/watch?v=4VAXv6yRULU
Inverse of a 2x2 Matrix:
https://www.youtube.com/watch?v=aiBgjz5xbyg
Inverse of a 3x3 Matrix:
https://www.youtube.com/watch?v=Fg7_mv3izR0
__________________________________
Determinant of 2x2 and 3x3 Matrix:
https://www.youtube.com/watch?v=3ROzG6n4yMc
Determinant of 4x4 Matrix:
https://www.youtube.com/watch?v=fWzUwrt1Z0s
Cramer's Rule - 2x2 Linear System:
https://www.youtube.com/watch?v=vXqlIOX2itM
Cramer's Rule - 3x3 Linear System:
https://www.youtube.com/watch?v=Ot87qLTODdQ
___________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
- published: 16 Feb 2018
- views: 2475620