Question

question 7 points 1

find (10b) if (b = \

$$\begin{bmatrix} 20 & 5 \\\\ 40 & 6 \\end{bmatrix}$$

).

\\(\bigcirc \

$$\begin{bmatrix} 200 & 50 \\\\ 400 & 60 \\end{bmatrix}$$

\\)

\\(\bigcirc \

$$\begin{bmatrix} -200 & 50 \\\\ -400 & 60 \\end{bmatrix}$$

\\)

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

<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
B =

$$\begin{bmatrix} 20 & 5 \\ 40 & 6 \end{bmatrix}$$

, \quad k = 10
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
10B =

$$\begin{bmatrix} 10 \times 20 & 10 \times 5 \\ 10 \times 40 & 10 \times 6 \end{bmatrix}$$

=

$$\begin{bmatrix} 200 & 50 \\ 400 & 60 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-correct>\(

$$\begin{bmatrix} 200 & 50 \\ 400 & 60 \end{bmatrix}$$

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

$$\begin{bmatrix} -200 & 50 \\ -400 & 60 \end{bmatrix}$$

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

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

<reasoning>

Identify the given matrix and scalar

Using the Scalar Multiplication knowledge point
\[
B =

$$\begin{bmatrix} 20 & 5 \\ 40 & 6 \end{bmatrix}$$

, \quad k = 10
\]

Multiply each element by the scalar

Using the Scalar Multiplication knowledge point
\[
10B =

$$\begin{bmatrix} 10 \times 20 & 10 \times 5 \\ 10 \times 40 & 10 \times 6 \end{bmatrix}$$

=

$$\begin{bmatrix} 200 & 50 \\ 400 & 60 \end{bmatrix}$$

\]
</reasoning>

<answer>
<mcq-correct>\(

$$\begin{bmatrix} 200 & 50 \\ 400 & 60 \end{bmatrix}$$

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

$$\begin{bmatrix} -200 & 50 \\ -400 & 60 \end{bmatrix}$$

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

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