Solve the Problem $T : R ^ { 2 } \rightarrow \mathscr { R } ^ { 2 }$

question 5

Multiple Choice

Solve the problem.
-Let $T : R ^ { 2 } \rightarrow \mathscr { R } ^ { 2 }$ be a linear transformation that maps $\mathbf { u } = \left[ \begin{array} { r } - 6 \\ 4 \end{array} \right]$ into $\left[ \begin{array} { r } - 22 \\ 12 \end{array} \right]$ and maps $\mathbf { v } = \left[ \begin{array} { r } 2 \\ - 5 \end{array} \right]$ into $\left[ \begin{array} { c } 11 \\ - 4 \end{array} \right]$ .
Use the fact that $T$ is linear to find the image of $3 \mathbf { u } + \mathbf { v }$ .

• A)
• \(\left[ \begin{array} { r } - 33 \\ 24 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { r } - 11 \\ 8 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { r } - 55 \\ 32 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { r } - 16 \\ 7 \end{array} \right]\)

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