Answer
a. k=$5$
b. k=$1$
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 $1\times 5$ matrix.
$m=1, n=5$
a.
" null space ... is a subspace of $\mathbb{R}^{n}$"
k=$5$
b.
"column space ... is a subspace of $\mathbb{R}^{m}$"
k=$1$
