#1
Let A be a m*n matrix and B an n*k matrix. If AB=0,
prove than rank A+rank B <=n.

#2
Let A be a m*n matrix with rank A=m, B be an n*(n-m) matrix, with rank B=(n-m).
If AB=0, and X in R^m is a solution to the linear system AX=0,prove there exists a unique Y in R^{n-m} such that X=BY.