-Suppose $B = \left\{ b _ { 1 } , b _ { 2 } , b _ { 3 } \right\}$

question 10

Multiple Choice

$$\text { Find the matrix of the linear transformation } \mathrm { T } : \mathrm { V } \rightarrow \mathrm { W } \text { relative to } \mathrm { B } \text { and } \mathrm { C } \text {. }$$
-Suppose $B = \left\{ b _ { 1 } , b _ { 2 } , b _ { 3 } \right\}$ is a basis for $V$ and $C = \left\{ c _ { 1 } , c _ { 2 } \right\}$ is a basis for $W$ . Let $T$ be defined by
$$\begin{array} { l } \mathrm { T } \left( \mathbf { b } _ { 1 } \right) = 3 \mathbf { c } _ { 1 } + \mathrm { c } _ { 2 } \\\mathrm {~T} \left( \mathbf { b } _ { 2 } \right) = 8 \mathbf { c } _ { 1 } - 8 \mathbf { c } _ { 2 } \\\mathrm {~T} \left( \mathbf { b } _ { 3 } \right) = 3 \mathbf { c } _ { 1 } + 2 \mathbf { c } _ { 2 }\end{array}$$

• A)
• \(\left[ \begin{array} { r r r } 4 & 0 & 5 \\ 1 & - 8 & 2 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { r r r } 3 & 8 & 3 \\ 1 & - 8 & 2 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { r r } 3 & 1 \\ 8 & - 8 \\ 3 & 2 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { l l } 3 & 4 \\ 8 & 0 \\ 3 & 5 \end{array} \right]\)

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