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

question 18

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.

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