Solve the Problem $\mathrm { T }$ Be the Linear Transformation Whose Standard Matrix Is

question 14

Multiple Choice

Solve the problem.
-The table shows the amount (in g) of protein, carbohydrate, and fat supplied by one unit (100 g) of three different foods. Let $\mathrm { T }$ be the linear transformation whose standard matrix is
$$A = \left[ \begin{array} { r r r } 1 & - 2 & 3 \\- 1 & 3 & - 4 \\- 2 & - 9 & 5\end{array} \right]$$
Determine whether the linear transformation $\mathrm { T }$ is one-to-one and whether it maps $R ^ { 3 }$ onto $R ^ { 3 }$ .

• A) Not one-to-one; onto \(R ^ { 3 }\)
• B) One-to-one; onto \(R ^ { 3 }\)
• C) Not one-to-one; not onto \(R ^ { 3 }\)
• D) One-to-one; not onto \(\mathfrak { R } ^ { 3 }\)

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Definitions:

Segment CM Ratio

The ratio of a business segment's contribution margin to its sales, indicating the profitability and efficiency of that segment.

Traceable Fixed Expenses

Fixed costs that can be directly associated with a specific department or product.

Common Fixed Expenses

Common fixed expenses refer to the overhead costs not directly linked to production or sales volume, shared across different departments or product lines.

Absorption Costing

An approach in accounting where the cost of a product is determined by including direct materials, direct labor, and all manufacturing overhead costs, whether variable or fixed.