Consider a matrix A, and let B = rref(A).(adsbygoogle = window.adsbygoogle || []).push({});

Is ker(A) necesarily equal to ker(B), and is im(A) necessarily equal to im(B)?

I want to say that the answer to both questions are yes because A and B are the same matrix, i.e. there are a finite number of elementary operations that can change A to B, and vice versa. Therefore, if they are the same matrices, then they necessarily will have the same kernel and image as each other.

Is my reasoning correct?

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# Kernels and Images for matrix

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