-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:

Volume of Units

The total number of individual units produced or sold by a business in a specified period.

General & Administrative Expenses

Operating expenses that are not directly tied to the production of goods or services, including salaries of non-sales personnel, rent, and office supplies.

WIP Inventory

Work-in-process inventory, which represents the costs of unfinished goods in manufacturing processes.

Finished Goods Inventory

The stock of completed products ready for sale, reflecting the end-stage of the production process.