Prove that pre-multiplying a matrix A m by the elementary matrix obtained with any matrix...

Cristopher Knox

Cristopher Knox

Answered

2022-07-01

Prove that pre-multiplying a matrix A m by the elementary matrix obtained with any matrix elementary line transformation I m l 1 l 2 E is the same as applying said elementary line transformation on the matrix A m

Answer & Explanation

Alexzander Bowman

Alexzander Bowman

Expert

2022-07-02Added 19 answers

Let e 1 , , e n be the standard basis row vectors, and observe the following facts about matrix multiplication:
1. e i A gives the ith row of the matrix A
2. For row vectors v 1 , , v m , we have
(   v 1   v m ) A = (   v 1 A   v m A )
Combine these to get the desired result for any elementary row operations.

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