Question

question 9 points 1

find \\(4c\\) if \\(c = \

$$\begin{bmatrix} 3 & 4 & 5 \\\\ 6 & 5 & 4 \\end{bmatrix}$$

\\).

\\(\bigcirc \

$$\begin{bmatrix} 12 & 16 & 20 \\\\ 24 & 20 & 16 \\end{bmatrix}$$

\\)

\\(\bigcirc \

$$\begin{bmatrix} 3 & 4 & 5 \\\\ 6 & 5 & 4 \\end{bmatrix}$$

\\)

Explanation:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
C =

$$\begin{bmatrix} 3 & 4 & 5 \\ 6 & 5 & 4 \end{bmatrix}$$

, \quad k = 4
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
4C =

$$\begin{bmatrix} 4 \times 3 & 4 \times 4 & 4 \times 5 \\ 4 \times 6 & 4 \times 5 & 4 \times 4 \end{bmatrix}$$

=

$$\begin{bmatrix} 12 & 16 & 20 \\ 24 & 20 & 16 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-correct>\(

$$\begin{bmatrix} 12 & 16 & 20 \\ 24 & 20 & 16 \end{bmatrix}$$

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

$$\begin{bmatrix} 3 & 4 & 5 \\ 6 & 5 & 4 \end{bmatrix}$$

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

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

Answer:

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<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
C =

$$\begin{bmatrix} 3 & 4 & 5 \\ 6 & 5 & 4 \end{bmatrix}$$

, \quad k = 4
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
4C =

$$\begin{bmatrix} 4 \times 3 & 4 \times 4 & 4 \times 5 \\ 4 \times 6 & 4 \times 5 & 4 \times 4 \end{bmatrix}$$

=

$$\begin{bmatrix} 12 & 16 & 20 \\ 24 & 20 & 16 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-correct>\(

$$\begin{bmatrix} 12 & 16 & 20 \\ 24 & 20 & 16 \end{bmatrix}$$

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

$$\begin{bmatrix} 3 & 4 & 5 \\ 6 & 5 & 4 \end{bmatrix}$$

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

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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Scalar Multiplication"
]
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