Question

question 34 points 1

consider \\(y = \

$$\begin{bmatrix} 0 & 0 & 0 \\\\ 0 & 0 & 0 \\\\ 0 & 0 & 0 \\end{bmatrix}$$

\\), \\(x = \

$$\begin{bmatrix} 1 & 3 & 7 \\\\ 2 & 2 & 8 \\\\ 1 & 6 & 9 \\end{bmatrix}$$

\\). find \\(yx\\).

• y
• x

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

<reasoning>

Identify the given matrices

Using the Matrix Multiplication knowledge point
\[
Y =

$$\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$$

, \quad X =

$$\begin{bmatrix} 1 & 3 & 7 \\ 2 & 2 & 8 \\ 1 & 6 & 9 \end{bmatrix}$$

\]

Compute the product YX

Using the Matrix Multiplication knowledge point
\[
YX =

$$\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$$

$$\begin{bmatrix} 1 & 3 & 7 \\ 2 & 2 & 8 \\ 1 & 6 & 9 \end{bmatrix}$$

=

$$\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$$

= Y
\]
</reasoning>

<answer>
<mcq-correct>(A) \(Y\)</mcq-correct>
<mcq-option>(B) \(X\)</mcq-option>
</answer>

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

<reasoning>

Identify the given matrices

Using the Matrix Multiplication knowledge point
\[
Y =

$$\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$$

, \quad X =

$$\begin{bmatrix} 1 & 3 & 7 \\ 2 & 2 & 8 \\ 1 & 6 & 9 \end{bmatrix}$$

\]

Compute the product YX

Using the Matrix Multiplication knowledge point
\[
YX =

$$\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$$

$$\begin{bmatrix} 1 & 3 & 7 \\ 2 & 2 & 8 \\ 1 & 6 & 9 \end{bmatrix}$$

=

$$\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$$

= Y
\]
</reasoning>

<answer>
<mcq-correct>(A) \(Y\)</mcq-correct>
<mcq-option>(B) \(X\)</mcq-option>
</answer>

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