Question

question 36 points 1
consider \\(a = \

$$\begin{bmatrix} 2 & 3 \\\\ 4 & 5 \\end{bmatrix}$$

\\), \\(b = \

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

\\). find \\(ab\\).

\\(\circ \

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

\\)
\\(\circ \

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

\\)

Explanation:

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<reasoning>

Identify the given matrices

Using the Matrix Multiplication knowledge point
\[
A =

$$\begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$$

, \quad B =

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

\]

Compute the product AB

Using the Matrix Multiplication knowledge point
\[
AB =

$$\begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$$

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

=

$$\begin{bmatrix} 2(0) + 3(0) & 2(0) + 3(0) \\ 4(0) + 5(0) & 4(0) + 5(0) \end{bmatrix}$$

=

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

\]
</reasoning>

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

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

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

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

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

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"Mathematics",
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Answer:

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<reasoning>

Identify the given matrices

Using the Matrix Multiplication knowledge point
\[
A =

$$\begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$$

, \quad B =

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

\]

Compute the product AB

Using the Matrix Multiplication knowledge point
\[
AB =

$$\begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$$

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

=

$$\begin{bmatrix} 2(0) + 3(0) & 2(0) + 3(0) \\ 4(0) + 5(0) & 4(0) + 5(0) \end{bmatrix}$$

=

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

\]
</reasoning>

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

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

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

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

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

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"question_type": "Multiple Choice",
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"Mathematics",
"Algebra",
"Matrix Multiplication"
]
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