Question 1
Determine if the vector u is in the column space of matrix A and whether it is in the null space of A.
$\mathbf{u} = \begin{bmatrix} 2 \ 3 \ -2 \end{bmatrix}$, $A = \begin{bmatrix} 1 & -3 & 4 \ 1 & 0 & -5 \ 3 & -3 & 6 \end{bmatrix}$
\text{Not in Col } A, \text{ not in Nul } A
\text{Not in Col } A, \text{ in Nul } A
\text{In Col } A \text{ and in Nul } A
\text{In Col } A, \text{ not in Nul } A