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Matrix Proof : Row Equivalence

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2. Write a matrix algebra proof for the following statement: Let A and B be nxm matrices. If A is row equivalent to B, then B is row equivalent to A. Show work.

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A matrix proof is provided in the solution.

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We say that the matrices A and C are row-equivalent if one can be obtained from the other by a succession of operations of the following kinds:

1-interchanging two rows;

2-multiplying a row by a non-zero constant;

3-replacing a row by the sum of it and (a non-zero multiple of) another ...

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