Question

question 21 points 2

if \\( b = \

$$\begin{bmatrix} 4 & -1 \\\\ 7 & 3 \\end{bmatrix}$$

\\), then find \\( |b| \\) (the determinant of b).

\\( \bigcirc \\) 5

\\( \bigcirc \\) 19

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

<reasoning>

Identify the given matrix

Using the Matrix Determinant knowledge point
\[
B =

$$\begin{bmatrix} 4 & -1 \\ 7 & 3 \end{bmatrix}$$

\]

Apply the determinant formula

Using the Matrix Determinant knowledge point
\[

$$\begin{aligned} |B| &= (4)(3) - (-1)(7) \\ &= 12 - (-7) \\ &= 12 + 7 \\ &= 19 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>5</mcq-option>
<mcq-correct>19</mcq-correct>
</answer>

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

<reasoning>

Identify the given matrix

Using the Matrix Determinant knowledge point
\[
B =

$$\begin{bmatrix} 4 & -1 \\ 7 & 3 \end{bmatrix}$$

\]

Apply the determinant formula

Using the Matrix Determinant knowledge point
\[

$$\begin{aligned} |B| &= (4)(3) - (-1)(7) \\ &= 12 - (-7) \\ &= 12 + 7 \\ &= 19 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>5</mcq-option>
<mcq-correct>19</mcq-correct>
</answer>

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