Answer
a. k=3
b. k=4
Work Step by Step
Theorem 2, p.201:
The null space of an m$\times$n matrix A is a subspace of $\mathbb{R}^{n}$.
Theorem 3, p.203:
The column space of an m$\times$n matrix A is a subspace of $\mathbb{R}^{m}$.
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$A$ is a $4\times 3$ matrix.
$m=4, n=3$
a.
" null space ... is a subspace of $\mathbb{R}^{n}$"
k=3
b.
"column space ... is a subspace of $\mathbb{R}^{m}$"
k=4
