Question

question 24 points 1

find \\(a - b\\).

\\a = \

$$\begin{bmatrix} 3 & 6 \\\\ 5 & 8 \\\\ -2 & 9 \\end{bmatrix}$$

\quad b = \

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

\\

• \\(\

$$\begin{bmatrix} 19 & 5 \\\\ 15 & -1 \\\\ -10 & 6 \\end{bmatrix}$$

\\)

• \\(\

$$\begin{bmatrix} 9 & 5 \\\\ 5 & -1 \\\\ -10 & 6 \\end{bmatrix}$$

\\)

Explanation:

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"current_concepts": [
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<reasoning>

Identify the given matrices

Using the Matrix Addition knowledge point
\[
A =

$$\begin{bmatrix} 3 & 6 \\ 5 & 8 \\ -2 & 9 \end{bmatrix}$$

, \quad B =

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

\]

Perform element-wise subtraction

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

$$\begin{bmatrix} 3 - (-6) & 6 - 1 \\ 5 - 0 & 8 - 9 \\ -2 - 8 & 9 - 3 \end{bmatrix}$$

\]

Simplify the elements

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

$$\begin{bmatrix} 9 & 5 \\ 5 & -1 \\ -10 & 6 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 19 & 5 \\ 15 & -1 \\ -10 & 6 \end{bmatrix}$$

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

$$\begin{bmatrix} 9 & 5 \\ 5 & -1 \\ -10 & 6 \end{bmatrix}$$

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

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

Answer:

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"multiple_choice_formatter",
"explain_then_answer",
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"Matrix Addition"
],
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"current_concepts": [
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<reasoning>

Identify the given matrices

Using the Matrix Addition knowledge point
\[
A =

$$\begin{bmatrix} 3 & 6 \\ 5 & 8 \\ -2 & 9 \end{bmatrix}$$

, \quad B =

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

\]

Perform element-wise subtraction

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

$$\begin{bmatrix} 3 - (-6) & 6 - 1 \\ 5 - 0 & 8 - 9 \\ -2 - 8 & 9 - 3 \end{bmatrix}$$

\]

Simplify the elements

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

$$\begin{bmatrix} 9 & 5 \\ 5 & -1 \\ -10 & 6 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 19 & 5 \\ 15 & -1 \\ -10 & 6 \end{bmatrix}$$

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

$$\begin{bmatrix} 9 & 5 \\ 5 & -1 \\ -10 & 6 \end{bmatrix}$$

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

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