Solve the Problem $A = \left[ \begin{array} { r r r } 1 & - 3 & 2 \\ - 3 & 4 & - 1 \\ 2 & - 5 & 3 \end{array} \right]$

Multiple Choice

Solve the problem.
-Let $A = \left[ \begin{array} { r r r } 1 & - 3 & 2 \\ - 3 & 4 & - 1 \\ 2 & - 5 & 3 \end{array} \right]$ and $\mathbf { b } = \left[ \begin{array} { r } 2 \\ 4 \\ - 4 \end{array} \right]$ .
Define a transformation $\mathrm { T } : \mathfrak { R } ^ { 3 } \rightarrow \mathbb { R } ^ { 3 }$ by $\mathrm { T } ( \mathrm { x } ) = \mathrm { Ax }$ .
If possible, find a vector $\mathbf { x }$ whose image under $\mathrm { T }$ is $\mathbf { b }$ . Otherwise, state that $\mathbf { b }$ is not in the range of the transformation $\mathrm { T }$ .

A)
$\left[ \begin{array} { l } 4 \\ 2 \\ 2 \end{array} \right]$
B)
$\left[ \begin{array} { l } 4 \\ 4 \\ 0 \end{array} \right]$
C)
$$\left[ \begin{array} { r } 4 \\0 \\- 4\end{array} \right]$$
D) $\mathbf { b }$ is not in the range of the transformation T.