Question

question 4 points 1

find (3q) if (q = \

$$\begin{bmatrix} 1 & 5 & 9 \\\\ 7 & 5 & 3 \\end{bmatrix}$$

).

\\(\bigcirc \

$$\begin{bmatrix} -3 & 15 & -27 \\\\ 21 & 15 & 9 \\end{bmatrix}$$

\\)

\\(\bigcirc \

$$\begin{bmatrix} 3 & 15 & 27 \\\\ 21 & 15 & 9 \\end{bmatrix}$$

\\)

Explanation:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
Q =

$$\begin{bmatrix} 1 & 5 & 9 \\ 7 & 5 & 3 \end{bmatrix}$$

, \quad k = 3
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
3Q =

$$\begin{bmatrix} 3 \cdot 1 & 3 \cdot 5 & 3 \cdot 9 \\ 3 \cdot 7 & 3 \cdot 5 & 3 \cdot 3 \end{bmatrix}$$

=

$$\begin{bmatrix} 3 & 15 & 27 \\ 21 & 15 & 9 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(

$$\begin{bmatrix} -3 & 15 & -27 \\ 21 & 15 & 9 \end{bmatrix}$$

\)</mcq-option>
<mcq-correct>(B) \(

$$\begin{bmatrix} 3 & 15 & 27 \\ 21 & 15 & 9 \end{bmatrix}$$

\)</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Scalar Multiplication"
]
}
</post_analysis>

Answer:

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"step_cot",
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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
Q =

$$\begin{bmatrix} 1 & 5 & 9 \\ 7 & 5 & 3 \end{bmatrix}$$

, \quad k = 3
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
3Q =

$$\begin{bmatrix} 3 \cdot 1 & 3 \cdot 5 & 3 \cdot 9 \\ 3 \cdot 7 & 3 \cdot 5 & 3 \cdot 3 \end{bmatrix}$$

=

$$\begin{bmatrix} 3 & 15 & 27 \\ 21 & 15 & 9 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(

$$\begin{bmatrix} -3 & 15 & -27 \\ 21 & 15 & 9 \end{bmatrix}$$

\)</mcq-option>
<mcq-correct>(B) \(

$$\begin{bmatrix} 3 & 15 & 27 \\ 21 & 15 & 9 \end{bmatrix}$$

\)</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Scalar Multiplication"
]
}
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