## problem on rank

#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 $X=BY$.