(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove or disprove with counter example:

If A is an (n x n) matrix then range(A) = range(A^T)

2. Relevant equations

Range = { y in R^N, y = Ax}

3. The attempt at a solution

I thought that the range(A) = the row space of (A^T) however whenever I tried examples to disprove this statement like:

1 2 3

4 5 6

7 8 9

And then transposed it and found the solution to y = Ax and y = A^Tx I got that both of the range was z - x - 2y = 0

Help?

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# Homework Help: Range/column space

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