Solve the Problem $\mathrm { A } = \left[ \begin{array} { r r r } 1 & - 3 & 0 \\ - 4 & 0 & 2 \\ 4 & 1 & - 2 \end{array} \right]$

Multiple Choice

Solve the problem.
-Let $\mathrm { A } = \left[ \begin{array} { r r r } 1 & - 3 & 0 \\ - 4 & 0 & 2 \\ 4 & 1 & - 2 \end{array} \right]$ and $\mathbf { b } = \left[ \begin{array} { r } 9 \\ - 6 \\ 4 \end{array} \right]$ .
Define a transformation $\mathrm { T }$ : $\mathfrak { R } ^ { 3 } \rightarrow \mathbb { R } ^ { 3 }$ by $\mathrm { T } ( \mathbf { x } ) = \mathrm { Ax }$ .
If possible, find a vector $x$ whose image under $\mathrm { T }$ is $\mathbf { b }$ . Otherwise, state that $\mathbf { b }$ is not in the range of the transformation $\mathrm { T }$ .

A)
$$\left[ \begin{array} { r } 3 \\- 2 \\0\end{array} \right]$$
B) $\mathbf { b }$ is not in the range of the transformation $T$ .
C) $\left[ \begin{array} { r } 3 \\ 3 \\ - 2 \end{array} \right]$
D)
$$\left[ \begin{array} { r } 3 \\- 2 \\3\end{array} \right]$$