Linear Algebra 13c: The Inverse of an Elementary Matrix

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Комментарии
Автор

Absolutely beautiful! Thank you Prof Grinfeld, you are such a great teacher! :D

lochestnut
Автор

Intuitively it feels right , that looking for matrix B which is an inverse of elementary matrix A, indeed one can look for such B that will "undo" what A "do" (to I -dentity matrix) .
But to explain it to myself more formally, it helped me to introduce temporarily one more I- matrix in the game, and to group two last matrices together.
To look at the product of 3 matrices [A] [ [B][ I ] ] = I makes it (to me) more clear that matrix A "undo" on matrix [B][I ] all the actions that B "did" to I, so I is restored hence the result equals I .Finely since [B] [ I] =I , the I in the left wing I can be dropped and from what remains, per definition A, B are inverses of each other .

sergelifshitz
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5:15 This reminds me of Dr. Seuss - are you having trouble saying this stuff? I just look in a mirror and I see what I say, then I say what I see.

solfeinberg