Consider an n x m matrix A. Find dim(im(A)) + dim(ker(A^T)), in terms of m and n.

I think this is equal to rank(A) + nullity(A^T). If so, I'm not sure what nullity(A^T) is equal to and how to the answer to this equation in terms of m and n.

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- Oct 29th 2009, 12:37 PMnoles2188dimension of image and kernel
Consider an n x m matrix A. Find dim(im(A)) + dim(ker(A^T)), in terms of m and n.

I think this is equal to rank(A) + nullity(A^T). If so, I'm not sure what nullity(A^T) is equal to and how to the answer to this equation in terms of m and n. - Oct 30th 2009, 06:03 AMHallsofIvy