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

question 18

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 $B = \left\{ b _ { 1 } , b _ { 2 } \right\}$ is a basis for $V$ and $C = \left\{ c _ { 1 } , c _ { 2 } , c _ { 3 } \right\}$ is a basis for $W$ . Let $T$ be defined by
$$\begin{array} { l } \mathrm { T } \left( \mathbf { b } _ { 1 } \right) = 5 c _ { 1 } + 6 c _ { 2 } - 5 c _ { 3 } \\T \left( b _ { 2 } \right) = 5 c _ { 1 } + 12 c _ { 2 } + 7 c _ { 3 }\end{array}$$

• A)
• \(\left[\begin{array}{rr}
• 5 & 5 \\
• 6 & 12 \\
• -5 & 7
• \end{array}\right]\)
• B)
• \[\left[ \begin{array} { r r }
• 5 & 5 \\
• 6 & 12 \\
• - 5 & 7
• \end{array} \right]\]
• C)
• \(\left[\begin{array}{rr}
• 5 & 0 \\
• 6 & 6 \\
• -5 & 12
• \end{array}\right]\)
• D)
• \(\left[\begin{array}{rrr}
• 5 & 6 & -5 \\
• 5 & 12 & 7
• \end{array}\right]\)

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Definitions:

South Carolina

A state in the southeastern region of the United States, known for its historical significance, including its role in the American Civil War.

New England

A region located in the northeastern corner of the United States comprising six states: Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont, known for its colonial history, distinct seasons, and cultural heritage.

Triangular Trade

A historical trade system in the 16th through 19th centuries involving the transatlantic slave trade among Europe, Africa, and the Americas.

Enslaved Africans

Describes Africans who were forcibly taken from their homeland and subjected to slavery, primarily in the Americas and Europe, from the 16th to the 19th centuries.