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Linear Algebra - Lecture 25 - The Invertible Matrix Theorem
12:02
YouTubeJames Hamblin
Linear Algebra - Lecture 25 - The Invertible Matrix Theorem
In this lecture, we discuss The Invertible Matrix Theorem, which is a list of 12 equivalent statements that classify when a square matrix is invertible.
49.5K viewsJun 9, 2018
Invertible Matrix Examples
4. (9 points) Give examples of A and B such that(a) A B is not invertible although A and B are invertible.(b) A B is invertible although A and B are not invertible(c) All of A, B and A B are invertible.(d) In the last case, show that B^-1 A^-1 is also invertible and find a formula for its inverse.(Hint: Check this out A^-1(A B)B^-1)
4. (9 points) Give examples of A and B such that(a) A B is not invertible although A and B are invertible.(b) A B is invertible although A and B are not invertible(c) All of A, B and A B are invertible.(d) In the last case, show that B^-1 A^-1 is also invertible and find a formula for its inverse.(Hint: Check this out A^-1(A B)B^-1)
numerade.com
Feb 21, 2022
How to Determine if a Matrix is invertible | Precalculus | Study.com
How to Determine if a Matrix is invertible | Precalculus | Study.com
study.com
Jul 20, 2021
Singular Matrix | Definition, Properties & Example
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Singular Matrix | Definition, Properties & Example
Study.com
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