Question

question 28 points 1

find: \\(\

$$\begin{bmatrix} 2 \\\\ 4 \\end{bmatrix}$$

+ \

$$\begin{bmatrix} 5 \\\\ 6 \\end{bmatrix}$$

= ?\\)

\\(\circ \

$$\begin{bmatrix} 7 \\\\ 10 \\end{bmatrix}$$

\\)

\\(\circ \

$$\begin{bmatrix} -7 \\\\ 10 \\end{bmatrix}$$

\\)

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 Addition"
],
"new_concepts": [],
"current_concepts": [
"Matrix Addition",
"Matrix Dimensions"
]
}
</pre_analysis>

<reasoning>

Identify the given matrices

Using the Matrix Addition knowledge point
\[
A =

$$\begin{bmatrix} 2 \\ 4 \end{bmatrix}$$

, \quad B =

$$\begin{bmatrix} 5 \\ 6 \end{bmatrix}$$

\]

Add corresponding elements

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

$$\begin{bmatrix} 2 + 5 \\ 4 + 6 \end{bmatrix}$$

=

$$\begin{bmatrix} 7 \\ 10 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 7 \\ 10 \end{bmatrix}$$

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

$$\begin{bmatrix} -7 \\ 10 \end{bmatrix}$$

\)</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 Addition"
],
"new_concepts": [],
"current_concepts": [
"Matrix Addition",
"Matrix Dimensions"
]
}
</pre_analysis>

<reasoning>

Identify the given matrices

Using the Matrix Addition knowledge point
\[
A =

$$\begin{bmatrix} 2 \\ 4 \end{bmatrix}$$

, \quad B =

$$\begin{bmatrix} 5 \\ 6 \end{bmatrix}$$

\]

Add corresponding elements

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

$$\begin{bmatrix} 2 + 5 \\ 4 + 6 \end{bmatrix}$$

=

$$\begin{bmatrix} 7 \\ 10 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 7 \\ 10 \end{bmatrix}$$

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

$$\begin{bmatrix} -7 \\ 10 \end{bmatrix}$$

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

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