Question

if \\( a = \

$$\begin{bmatrix} 5 & 9 & 2 \\\\ 1 & 7 & 6 \\\\ 3 & 4 & 8 \\end{bmatrix}$$

\\), then find \\( 6a \\).

\\( \bigcirc \

$$\begin{bmatrix} 10 & 18 & 4 \\\\ 2 & 14 & 12 \\\\ 6 & 8 & 16 \\end{bmatrix}$$

\\)

\\( \bigcirc \

$$\begin{bmatrix} 30 & 54 & 12 \\\\ 6 & 42 & 36 \\\\ 18 & 24 & 48 \\end{bmatrix}$$

\\)

Explanation:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
A =

$$\begin{bmatrix} 5 & 9 & 2 \\ 1 & 7 & 6 \\ 3 & 4 & 8 \end{bmatrix}$$

, \quad k = 6
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
6A =

$$\begin{bmatrix} 6(5) & 6(9) & 6(2) \\ 6(1) & 6(7) & 6(6) \\ 6(3) & 6(4) & 6(8) \end{bmatrix}$$

=

$$\begin{bmatrix} 30 & 54 & 12 \\ 6 & 42 & 36 \\ 18 & 24 & 48 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 10 & 18 & 4 \\ 2 & 14 & 12 \\ 6 & 8 & 16 \end{bmatrix}$$

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

$$\begin{bmatrix} 30 & 54 & 12 \\ 6 & 42 & 36 \\ 18 & 24 & 48 \end{bmatrix}$$

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

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

Answer:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
A =

$$\begin{bmatrix} 5 & 9 & 2 \\ 1 & 7 & 6 \\ 3 & 4 & 8 \end{bmatrix}$$

, \quad k = 6
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
6A =

$$\begin{bmatrix} 6(5) & 6(9) & 6(2) \\ 6(1) & 6(7) & 6(6) \\ 6(3) & 6(4) & 6(8) \end{bmatrix}$$

=

$$\begin{bmatrix} 30 & 54 & 12 \\ 6 & 42 & 36 \\ 18 & 24 & 48 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 10 & 18 & 4 \\ 2 & 14 & 12 \\ 6 & 8 & 16 \end{bmatrix}$$

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

$$\begin{bmatrix} 30 & 54 & 12 \\ 6 & 42 & 36 \\ 18 & 24 & 48 \end{bmatrix}$$

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

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