Hey, I was looking for help on these questions dealing with row and column spaces...(adsbygoogle = window.adsbygoogle || []).push({});

1. Prove that the linear system Ax = b is consistent IFF the rank of (A|b) equals the rank of A.

2. Show that if A and B are nxn matrices, and N(A-B) = R^n, then A = B

The first one I can't get much of a handle on. I can sort of feel like its going to have to do something with b lying in the column space of A? maybe? I can't quite get there. The second one I think I understand: N(0) corresponds to 0x = x, which is any vector in R^n, or something along those lines.

And also, I have a general question: If a matrix has linearly independent column vectors, under what conditions are its row vectors linearly independent?

Thanks for any help

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# Homework Help: Row and Column space questions.

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