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Intro to the Invertible Matrix Theorem and its 10 statements
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Intro to the Invertible Matrix Theorem and its 10 statements
15:43
About this lesson
• only works for \(n \times n\) square matrices
• If one is true, then they are all true
• If one is false, then they are all false
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Video 1 of 10
Intro to the Invertible Matrix Theorem and its 10 statements
16 min
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Applying the invertible matrix theorem with examples
8 min
Determining invertibility using column linear dependence
5 min
Checking invertibility of a 4x4 matrix using pivot positions
3 min
True or false: invertibility implies x to Ax maps Rn onto Rn
3 min
Proving CA=I implies AD=I using the invertible matrix theorem
2 min
Disproving "AX=0 has trivial solution implies A is not invertible"
3 min
Proving Ax=0 having a nontrivial solution implies A has less than n pivots
4 min
Why a square matrix with two identical rows is not invertible
11 min
Proving that if AB is invertible then B is invertible
7 min