Question

find \\(m + n\\).

\\m = \

$$\begin{bmatrix} 3 & 7 \\\\ 2 & 5 \\end{bmatrix}$$

\quad n = \

$$\begin{bmatrix} -3 & 2 \\\\ 4 & -1 \\end{bmatrix}$$

\\

• \\(\

$$\begin{bmatrix} 0 & 9 \\\\ 6 & 4 \\end{bmatrix}$$

\\)

• \\(\

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

\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Matrix Representation",
"Matrix Dimensions"
],
"new_concepts": [
"Matrix Addition"
],
"current_concepts": [
"Matrix Representation",
"Matrix Dimensions",
"Matrix Addition"
]
}
</pre_analysis>

<reasoning>

Identify matrix dimensions

Using the Matrix Dimensions knowledge point
\[
\text{Dim}(M) = 2 \times 2, \quad \text{Dim}(N) = 2 \times 2
\]

Perform matrix addition

Using the Matrix Representation knowledge point
\[
M + N =

$$\begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix}$$

+

$$\begin{bmatrix} -3 & 2 \\ 4 & -1 \end{bmatrix}$$

\]
\[
M + N =

$$\begin{bmatrix} 3 + (-3) & 7 + 2 \\ 2 + 4 & 5 + (-1) \end{bmatrix}$$

\]
\[
M + N =

$$\begin{bmatrix} 0 & 9 \\ 6 & 4 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 0 & 9 \\ 6 & 4 \end{bmatrix}$$

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

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

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

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Matrix Representation",
"Matrix Dimensions"
],
"new_concepts": [
"Matrix Addition"
],
"current_concepts": [
"Matrix Representation",
"Matrix Dimensions",
"Matrix Addition"
]
}
</pre_analysis>

<reasoning>

Identify matrix dimensions

Using the Matrix Dimensions knowledge point
\[
\text{Dim}(M) = 2 \times 2, \quad \text{Dim}(N) = 2 \times 2
\]

Perform matrix addition

Using the Matrix Representation knowledge point
\[
M + N =

$$\begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix}$$

+

$$\begin{bmatrix} -3 & 2 \\ 4 & -1 \end{bmatrix}$$

\]
\[
M + N =

$$\begin{bmatrix} 3 + (-3) & 7 + 2 \\ 2 + 4 & 5 + (-1) \end{bmatrix}$$

\]
\[
M + N =

$$\begin{bmatrix} 0 & 9 \\ 6 & 4 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 0 & 9 \\ 6 & 4 \end{bmatrix}$$

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

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

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

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