Linear Algebra 13c: The Inverse of an Elementary Matrix

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[@MathTheBeautiful]

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[@lochestnut]

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

[@sergelifshitz1034]

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 .

[@harryshen4454]

Great video! Easy to implement! 大师我悟了

[@trackmyactivity]

Amazing! Thank you very much

[@solfeinberg437]

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.

[@sergelifshitz1034]

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