Question

What is the relationship between the four fundamental subspaces of a matrix?

Answer 1

http://www.math.sunysb.edu/~badger/notes/4fund.pdf

Answer 2

dimension of column space of A = rank[A]
dimension of row space of A = rank[A]
dimension of nullspace of A = n - r
dimension of nullspace of A^T = m-r

Answer 3

alright now we have to make sure we find the final connection how they Col(A) = Row(A^t)