Question

question 1 points 1

let \\(m = \

$$\begin{bmatrix} 12 & 18 \\\\ 5 & 15 \\end{bmatrix}$$

\\). find \\(3m\\).

\\(\bigcirc \

$$\begin{bmatrix} 36 & 54 \\\\ 15 & 45 \\end{bmatrix}$$

\\)

\\(\bigcirc \

$$\begin{bmatrix} -36 & 54 \\\\ 15 & -45 \\end{bmatrix}$$

\\)

Explanation:

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<reasoning>

Identify the given matrix and operation

Using the Matrix Representation knowledge point
\[
M =

$$\begin{bmatrix} 12 & 18 \\ 5 & 15 \end{bmatrix}$$

, \quad k = 3
\]

Apply scalar multiplication to each element

Multiply every entry in the matrix by the scalar \(3\):
\[
3M =

$$\begin{bmatrix} 3 \times 12 & 3 \times 18 \\ 3 \times 5 & 3 \times 15 \end{bmatrix}$$

\]

Calculate the final matrix entries

Compute the products for each position:
\[
3M =

$$\begin{bmatrix} 36 & 54 \\ 15 & 45 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-correct>\(

$$\begin{bmatrix} 36 & 54 \\ 15 & 45 \end{bmatrix}$$

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

$$\begin{bmatrix} -36 & 54 \\ 15 & -45 \end{bmatrix}$$

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

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

Answer:

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"step_cot",
"multiple_choice_formatter",
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"tutor",
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"needs_drawing": false,
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"Matrix Representation"
],
"new_concepts": [
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],
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"Scalar Multiplication"
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</pre_analysis>

<reasoning>

Identify the given matrix and operation

Using the Matrix Representation knowledge point
\[
M =

$$\begin{bmatrix} 12 & 18 \\ 5 & 15 \end{bmatrix}$$

, \quad k = 3
\]

Apply scalar multiplication to each element

Multiply every entry in the matrix by the scalar \(3\):
\[
3M =

$$\begin{bmatrix} 3 \times 12 & 3 \times 18 \\ 3 \times 5 & 3 \times 15 \end{bmatrix}$$

\]

Calculate the final matrix entries

Compute the products for each position:
\[
3M =

$$\begin{bmatrix} 36 & 54 \\ 15 & 45 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-correct>\(

$$\begin{bmatrix} 36 & 54 \\ 15 & 45 \end{bmatrix}$$

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

$$\begin{bmatrix} -36 & 54 \\ 15 & -45 \end{bmatrix}$$

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

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