In linear algebra, an n-by-nsquare matrixA is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that
where In denotes the n-by-nidentity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A−1.
A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0. Singular matrices are rare in the sense that a square matrix randomly selected from a continuous uniform distribution on its entries will almost never be singular.
Non-square matrices (m-by-n matrices for which m ≠ n) do not have an inverse. However, in some cases such a matrix may have a left inverse or right inverse. If A is m-by-n and the rank of A is equal to n, then A has a left inverse: an n-by-m matrix B such that BA = I. If A has rank m, then it has a right inverse: an n-by-m matrix B such that AB = I.
Invertible matrices and determinants | Matrices | Precalculus | Khan Academy
An invertible matrix is a matrix that has an inverse. In this video, we investigate the relationship between a matrix's determinant, and whether that matrix is invertible.
published: 07 Apr 2021
Invertible and noninvertibles matrices
Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-intro-to-matrix-inverses/e/determine-inverse-matrices
Recognizing when a matrix is invertible or not.
published: 13 Aug 2018
Invertible matrix
Checking if a matrix is invertible using row-reduction, without finding A-1
Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw
Check out my Matrix Algebra playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmAIZGo2l8SWvsHeeCLzamx0
published: 19 Feb 2019
Inverse Matrices and Their Properties
We learned about matrix multiplication, so what about matrix division? There is no such thing! But we can multiply a matrix by its inverse, which is kind of like multiplying a number by its reciprocal, to cancel it out, which with matrices will yield the identity matrix. So how do you find an inverse matrix? Let's learn how!
Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath
Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio
EMAIL► [email protected]
PATREON► http://patreon.com/Prof...
published: 14 Jan 2019
Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra
How to think about linear systems of equations geometrically.
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
------------------
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 ne...
published: 15 Aug 2016
Inverse of a 3x3 Matrix
This precalculus video tutorial explains how to find the inverse of a 3x3 matrix. You need to write an augmented matrix containing the original matrix and the multiplicative identity matrix. You need to convert the original matrix into the multiplicative identity matrix using elementary row operations. The multiplicative identity matrix will change into the inverse of the original matrix as long as you apply the same elementary row operations to it.
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: ...
published: 19 Feb 2018
Invertible Matrix
Matrix A is invertible if we can find another matrix B of same order such that AB = I where I is the identity matrix of same order. A matrix is invertible only if it is a square matrix and its determinant is non zero
published: 19 Dec 2013
Class 12th – Overview of Invertible Matrices | Matrices | Tutorials Point
Overview of Invertible Matrices
Watch more videos at https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Er. Ridhi Arora, Tutorials Point India Private Limited.
published: 08 Feb 2018
Inverse of a 2x2 Matrix
This precalculus video tutorial explains how to determine the inverse of a 2x2 matrix. It provides a simple formula to determine the multiplicative inverse of a matrix. You can check to see if you have the right answer by multiplying the matrix and its inverse to see if you get the multiplicative identity matrix I2. This video contains plenty of examples and practice problems.
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 Matrice...
published: 18 Feb 2018
Linear Algebra 2.3.1 Characterizations of Invertible Matrices
An invertible matrix is a matrix that has an inverse. In this video, we investigate the relationship between a matrix's determinant, and whether that matrix is ...
An invertible matrix is a matrix that has an inverse. In this video, we investigate the relationship between a matrix's determinant, and whether that matrix is invertible.
An invertible matrix is a matrix that has an inverse. In this video, we investigate the relationship between a matrix's determinant, and whether that matrix is invertible.
Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-intro-to-matrix-inverses...
Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-intro-to-matrix-inverses/e/determine-inverse-matrices
Recognizing when a matrix is invertible or not.
Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-intro-to-matrix-inverses/e/determine-inverse-matrices
Recognizing when a matrix is invertible or not.
Checking if a matrix is invertible using row-reduction, without finding A-1
Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw
...
Checking if a matrix is invertible using row-reduction, without finding A-1
Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw
Check out my Matrix Algebra playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmAIZGo2l8SWvsHeeCLzamx0
Checking if a matrix is invertible using row-reduction, without finding A-1
Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw
Check out my Matrix Algebra playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmAIZGo2l8SWvsHeeCLzamx0
We learned about matrix multiplication, so what about matrix division? There is no such thing! But we can multiply a matrix by its inverse, which is kind of lik...
We learned about matrix multiplication, so what about matrix division? There is no such thing! But we can multiply a matrix by its inverse, which is kind of like multiplying a number by its reciprocal, to cancel it out, which with matrices will yield the identity matrix. So how do you find an inverse matrix? Let's learn how!
Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath
Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio
EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains
Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM
Barnes and Noble: https://bit.ly/3pUjmrn
Book Depository: http://bit.ly/3aOVDlT
We learned about matrix multiplication, so what about matrix division? There is no such thing! But we can multiply a matrix by its inverse, which is kind of like multiplying a number by its reciprocal, to cancel it out, which with matrices will yield the identity matrix. So how do you find an inverse matrix? Let's learn how!
Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath
Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio
EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains
Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM
Barnes and Noble: https://bit.ly/3pUjmrn
Book Depository: http://bit.ly/3aOVDlT
How to think about linear systems of equations geometrically.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support...
How to think about linear systems of equations geometrically.
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
------------------
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
How to think about linear systems of equations geometrically.
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
------------------
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
This precalculus video tutorial explains how to find the inverse of a 3x3 matrix. You need to write an augmented matrix containing the original matrix and the ...
This precalculus video tutorial explains how to find the inverse of a 3x3 matrix. You need to write an augmented matrix containing the original matrix and the multiplicative identity matrix. You need to convert the original matrix into the multiplicative identity matrix using elementary row operations. The multiplicative identity matrix will change into the inverse of the original matrix as long as you apply the same elementary row operations to it.
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
This precalculus video tutorial explains how to find the inverse of a 3x3 matrix. You need to write an augmented matrix containing the original matrix and the multiplicative identity matrix. You need to convert the original matrix into the multiplicative identity matrix using elementary row operations. The multiplicative identity matrix will change into the inverse of the original matrix as long as you apply the same elementary row operations to it.
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
Matrix A is invertible if we can find another matrix B of same order such that AB = I where I is the identity matrix of same order. A matrix is invertible only ...
Matrix A is invertible if we can find another matrix B of same order such that AB = I where I is the identity matrix of same order. A matrix is invertible only if it is a square matrix and its determinant is non zero
Matrix A is invertible if we can find another matrix B of same order such that AB = I where I is the identity matrix of same order. A matrix is invertible only if it is a square matrix and its determinant is non zero
Overview of Invertible Matrices
Watch more videos at https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Er. Ridhi Arora, Tutorials Point India ...
Overview of Invertible Matrices
Watch more videos at https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Er. Ridhi Arora, Tutorials Point India Private Limited.
Overview of Invertible Matrices
Watch more videos at https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Er. Ridhi Arora, Tutorials Point India Private Limited.
This precalculus video tutorial explains how to determine the inverse of a 2x2 matrix. It provides a simple formula to determine the multiplicative inverse of ...
This precalculus video tutorial explains how to determine the inverse of a 2x2 matrix. It provides a simple formula to determine the multiplicative inverse of a matrix. You can check to see if you have the right answer by multiplying the matrix and its inverse to see if you get the multiplicative identity matrix I2. This video contains plenty of examples and practice problems.
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
This precalculus video tutorial explains how to determine the inverse of a 2x2 matrix. It provides a simple formula to determine the multiplicative inverse of a matrix. You can check to see if you have the right answer by multiplying the matrix and its inverse to see if you get the multiplicative identity matrix I2. This video contains plenty of examples and practice problems.
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
An invertible matrix is a matrix that has an inverse. In this video, we investigate the relationship between a matrix's determinant, and whether that matrix is invertible.
Keep going! Check out the next lesson and practice what you’re learning:
https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-intro-to-matrix-inverses/e/determine-inverse-matrices
Recognizing when a matrix is invertible or not.
Checking if a matrix is invertible using row-reduction, without finding A-1
Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw
Check out my Matrix Algebra playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmAIZGo2l8SWvsHeeCLzamx0
We learned about matrix multiplication, so what about matrix division? There is no such thing! But we can multiply a matrix by its inverse, which is kind of like multiplying a number by its reciprocal, to cancel it out, which with matrices will yield the identity matrix. So how do you find an inverse matrix? Let's learn how!
Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath
Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio
EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains
Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM
Barnes and Noble: https://bit.ly/3pUjmrn
Book Depository: http://bit.ly/3aOVDlT
How to think about linear systems of equations geometrically.
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
------------------
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
This precalculus video tutorial explains how to find the inverse of a 3x3 matrix. You need to write an augmented matrix containing the original matrix and the multiplicative identity matrix. You need to convert the original matrix into the multiplicative identity matrix using elementary row operations. The multiplicative identity matrix will change into the inverse of the original matrix as long as you apply the same elementary row operations to it.
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
Matrix A is invertible if we can find another matrix B of same order such that AB = I where I is the identity matrix of same order. A matrix is invertible only if it is a square matrix and its determinant is non zero
Overview of Invertible Matrices
Watch more videos at https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Er. Ridhi Arora, Tutorials Point India Private Limited.
This precalculus video tutorial explains how to determine the inverse of a 2x2 matrix. It provides a simple formula to determine the multiplicative inverse of a matrix. You can check to see if you have the right answer by multiplying the matrix and its inverse to see if you get the multiplicative identity matrix I2. This video contains plenty of examples and practice problems.
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
In linear algebra, an n-by-nsquare matrixA is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that
where In denotes the n-by-nidentity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A−1.
A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0. Singular matrices are rare in the sense that a square matrix randomly selected from a continuous uniform distribution on its entries will almost never be singular.
Non-square matrices (m-by-n matrices for which m ≠ n) do not have an inverse. However, in some cases such a matrix may have a left inverse or right inverse. If A is m-by-n and the rank of A is equal to n, then A has a left inverse: an n-by-m matrix B such that BA = I. If A has rank m, then it has a right inverse: an n-by-m matrix B such that AB = I.