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:

Motivational Trait

Personal characteristics that influence an individual’s tendency to pursue goals with energy and persistence.

Emotional Stability

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A characteristic of personality marked by fluctuations in emotions, nervousness, changeable moods, quick temper, and feelings of sorrow.