Question

find the element \\(a_{31}\\) of the given matrix.
\\a = \

$$\begin{bmatrix} 2 & 0 & 3 \\\\ -1 & 3 & 6 \\\\ 8 & 9 & 4 \\end{bmatrix}$$

\\

\\(\bigcirc\\) 8
\\(\bigcirc\\) 2

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 Element Indexing"
],
"new_concepts": [],
"current_concepts": [
"Matrix Element Indexing",
"Matrix Terminology"
]
}
</pre_analysis>

<reasoning>

Identify the element index

Using the Matrix Element Indexing knowledge point
\[
a_{ij} \implies i = 3, \quad j = 1
\]

Locate the row and column

Using the Matrix Element Indexing knowledge point
\[
\text{Row } 3 =

$$\begin{bmatrix} 8 & 9 & 4 \end{bmatrix}$$

, \quad \text{Column } 1 =

$$\begin{bmatrix} 2 \\ -1 \\ 8 \end{bmatrix}$$

\]

Find the intersection element

Using the Matrix Element Indexing knowledge point
\[
a_{31} = 8
\]
</reasoning>

<answer>
<mcq-correct>(A) 8</mcq-correct>
<mcq-option>(B) 2</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Matrix Element Indexing"
]
}
</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 Element Indexing"
],
"new_concepts": [],
"current_concepts": [
"Matrix Element Indexing",
"Matrix Terminology"
]
}
</pre_analysis>

<reasoning>

Identify the element index

Using the Matrix Element Indexing knowledge point
\[
a_{ij} \implies i = 3, \quad j = 1
\]

Locate the row and column

Using the Matrix Element Indexing knowledge point
\[
\text{Row } 3 =

$$\begin{bmatrix} 8 & 9 & 4 \end{bmatrix}$$

, \quad \text{Column } 1 =

$$\begin{bmatrix} 2 \\ -1 \\ 8 \end{bmatrix}$$

\]

Find the intersection element

Using the Matrix Element Indexing knowledge point
\[
a_{31} = 8
\]
</reasoning>

<answer>
<mcq-correct>(A) 8</mcq-correct>
<mcq-option>(B) 2</mcq-option>
</answer>

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