Question

question 29 points 1

consider \\(i = \

$$\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix}$$

\\) and \\(b = \

$$\begin{bmatrix} 2 & 10 \\\\ 6 & 5 \\end{bmatrix}$$

\\). find \\(ib\\).

• \\(b\\)
• \\(i\\)
• cannot be determined
• all of the choices

Explanation:

<pre_analysis>
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"current_concepts": [
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<reasoning>

Identify the given matrices

Using the Matrix Multiplication knowledge point
\[
I =

$$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

, \quad B =

$$\begin{bmatrix} 2 & 10 \\ 6 & 5 \end{bmatrix}$$

\]

Compute the matrix product

Using the Matrix Multiplication knowledge point
\[
IB =

$$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

$$\begin{bmatrix} 2 & 10 \\ 6 & 5 \end{bmatrix}$$

=

$$\begin{bmatrix} 1(2) + 0(6) & 1(10) + 0(5) \\ 0(2) + 1(6) & 0(10) + 1(5) \end{bmatrix}$$

=

$$\begin{bmatrix} 2 & 10 \\ 6 & 5 \end{bmatrix}$$

= B
\]
</reasoning>

<answer>
<mcq-correct>(A) \(B\)</mcq-correct>
<mcq-option>(B) \(I\)</mcq-option>
<mcq-option>(C) Cannot be determined</mcq-option>
<mcq-option>(D) All of the choices</mcq-option>
</answer>

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

Answer:

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"step_cot",
"multiple_choice_formatter",
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"Matrix Multiplication"
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<reasoning>

Identify the given matrices

Using the Matrix Multiplication knowledge point
\[
I =

$$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

, \quad B =

$$\begin{bmatrix} 2 & 10 \\ 6 & 5 \end{bmatrix}$$

\]

Compute the matrix product

Using the Matrix Multiplication knowledge point
\[
IB =

$$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

$$\begin{bmatrix} 2 & 10 \\ 6 & 5 \end{bmatrix}$$

=

$$\begin{bmatrix} 1(2) + 0(6) & 1(10) + 0(5) \\ 0(2) + 1(6) & 0(10) + 1(5) \end{bmatrix}$$

=

$$\begin{bmatrix} 2 & 10 \\ 6 & 5 \end{bmatrix}$$

= B
\]
</reasoning>

<answer>
<mcq-correct>(A) \(B\)</mcq-correct>
<mcq-option>(B) \(I\)</mcq-option>
<mcq-option>(C) Cannot be determined</mcq-option>
<mcq-option>(D) All of the choices</mcq-option>
</answer>

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