Question

question 19 points 2

if \\(a = \

$$\begin{bmatrix} 3 & 7 \\\\ 8 & -5 \\end{bmatrix}$$

\\) and \\(b = \

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

\\), then find \\(a + b\\).

\\(\circ \

$$\begin{bmatrix} -2 & 5 \\\\ 6 & 1 \\end{bmatrix}$$

\\)

\\(\circ \

$$\begin{bmatrix} 2 & 5 \\\\ 6 & 1 \\end{bmatrix}$$

\\)

Explanation:

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

Identify the matrices and operation

Using the Matrix Addition knowledge point
\[
A =

$$\begin{bmatrix} 3 & 7 \\ 8 & -5 \end{bmatrix}$$

, \quad B =

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

\]
We need to find \(A + B\).

Perform element-wise addition

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

$$\begin{bmatrix} 3 + (-5) & 7 + (-2) \\ 8 + (-2) & -5 + 6 \end{bmatrix}$$

=

$$\begin{bmatrix} -2 & 5 \\ 6 & 1 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} -2 & 5 \\ 6 & 1 \end{bmatrix}$$

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

$$\begin{bmatrix} 2 & 5 \\ 6 & 1 \end{bmatrix}$$

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

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

Answer:

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"concepts_used": [
"Matrix Addition"
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"current_concepts": [
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<reasoning>

Identify the matrices and operation

Using the Matrix Addition knowledge point
\[
A =

$$\begin{bmatrix} 3 & 7 \\ 8 & -5 \end{bmatrix}$$

, \quad B =

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

\]
We need to find \(A + B\).

Perform element-wise addition

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

$$\begin{bmatrix} 3 + (-5) & 7 + (-2) \\ 8 + (-2) & -5 + 6 \end{bmatrix}$$

=

$$\begin{bmatrix} -2 & 5 \\ 6 & 1 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} -2 & 5 \\ 6 & 1 \end{bmatrix}$$

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

$$\begin{bmatrix} 2 & 5 \\ 6 & 1 \end{bmatrix}$$

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

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