Let $A=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ -3 -9 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 1 3 -3 -9 3 9

.

Find $k$ such that $Nul (A)$ is a subspace of ${\mathbb R}^k$

Find $k$ such that $Col (A)$ is a subspace of ${\mathbb R}^k$

Let $B=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\end{array}}\right[$ -5 4 -2 2 -2 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\end{array}}\right]$

.

Find $k$ such that $Row (B)$ is a subspace of ${\mathbb R}^k$

Find $k$ such that $Nul (B)$ is a subspace of ${\mathbb R}^k$

Let $C=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 8 3 0 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 3 0 -2 0 -2 8 -2 8 3

.

Find $k$ such that $Col (C)$ is a subspace of ${\mathbb R}^k$

Find $k$ such that $Row (C)$ is a subspace of ${\mathbb R}^k$