Linear Algebra - Lecture 25 - The Invertible Matrix Theorem
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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
SOLVED: Question 1. (5 points Give examples of matrices A and B such that(a) A B is not invertible; although A and B are invertible (6) A B is invertible, although A and B are not invertible.(c) all of A,B, and A B are invertible(d) How many 2 by 2 matrices are there whose entries are ls and Os?(e) Suppose 3 of the 4 entries in a 2 by 2 matrix are ls and the fourth entry is 0 Is this matrix invertible?
SOLVED: Question 1. (5 points Give examples of matrices A and B such that(a) A B is not invertible; although A and B are invertible (6) A B is invertible, although A and B are not invertible.(c) all of A,B, and A B are invertible(d) How many 2 by 2 matrices are there whose entries are ls and Os?(e) Suppose 3 of the 4 entries in a 2 by 2 matrix are ls and the fourth entry is 0 Is this matrix invertible?
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