Exercise 3.5.6

A: $\dim <!--\; FUNCTION\; APPLICATION\; -->2,2,2,1$ : Rows $(0,3,3,3)$ and $(0,1,0,1)$; columns $(3,0,1)$ and $(3,0,0)$; nullspace $(1,0,0,0)$ and $(0,-1,0,1);N\left(A^T\right)(0,1,0).B$ : $\dim <!--\; FUNCTION\; APPLICATION\; -->1,1,0,2$ Row space (1), column space $(1,4,5)$, nullspace: empty basis, $N\left(A^T\right)(-4,1,0)$ and $(-5,0,1)$.