Exercise 3.5.30

(a) $\mathit{AX}=0$ if each column of $X$ is a multiple of $(1,1,1);\dim <!--\; FUNCTION\; APPLICATION\; -->($ nullspace $)=3$.

(b) If $\mathit{AX}=B$ then all columns of $B$ add to zero; dimension of the $B$ ’s $=6$.

(c) $3+6=\dim <!--\; FUNCTION\; APPLICATION\; -->\left(M^{3\times 3}\right)=9$ entries in a 3 by 3 matrix.