Question

question 17 points 1

find \\(a + b\\).

\\a = \

$$\begin{bmatrix} 3 & 6 \\\\ 5 & 8 \\\\ -2 & 9 \\end{bmatrix}$$

\quad b = \

$$\begin{bmatrix} -6 & 1 \\\\ 0 & 9 \\\\ 8 & 3 \\end{bmatrix}$$

\\

• \\(\

$$\begin{bmatrix} -3 & 7 \\\\ 5 & 17 \\\\ 6 & 12 \\end{bmatrix}$$

\\)

• \\(\

$$\begin{bmatrix} 6 & 12 \\\\ 10 & 16 \\\\ -4 & 18 \\end{bmatrix}$$

\\)

Explanation:

<pre_analysis>
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"concepts_used": [
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"current_concepts": [
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<reasoning>

Identify the given matrices

Using the Matrix Addition knowledge point
\[
A =

$$\begin{bmatrix} 3 & 6 \\ 5 & 8 \\ -2 & 9 \end{bmatrix}$$

, \quad B =

$$\begin{bmatrix} -6 & 1 \\ 0 & 9 \\ 8 & 3 \end{bmatrix}$$

\]

Add corresponding elements

Using the Matrix Addition knowledge point
\[
A + B =

$$\begin{bmatrix} 3 + (-6) & 6 + 1 \\ 5 + 0 & 8 + 9 \\ -2 + 8 & 9 + 3 \end{bmatrix}$$

=

$$\begin{bmatrix} -3 & 7 \\ 5 & 17 \\ 6 & 12 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} -3 & 7 \\ 5 & 17 \\ 6 & 12 \end{bmatrix}$$

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

$$\begin{bmatrix} 6 & 12 \\ 10 & 16 \\ -4 & 18 \end{bmatrix}$$

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

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

Answer:

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"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
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"Matrix Addition"
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"current_concepts": [
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<reasoning>

Identify the given matrices

Using the Matrix Addition knowledge point
\[
A =

$$\begin{bmatrix} 3 & 6 \\ 5 & 8 \\ -2 & 9 \end{bmatrix}$$

, \quad B =

$$\begin{bmatrix} -6 & 1 \\ 0 & 9 \\ 8 & 3 \end{bmatrix}$$

\]

Add corresponding elements

Using the Matrix Addition knowledge point
\[
A + B =

$$\begin{bmatrix} 3 + (-6) & 6 + 1 \\ 5 + 0 & 8 + 9 \\ -2 + 8 & 9 + 3 \end{bmatrix}$$

=

$$\begin{bmatrix} -3 & 7 \\ 5 & 17 \\ 6 & 12 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} -3 & 7 \\ 5 & 17 \\ 6 & 12 \end{bmatrix}$$

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

$$\begin{bmatrix} 6 & 12 \\ 10 & 16 \\ -4 & 18 \end{bmatrix}$$

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

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