Question

question 33 points 1

consider \\(a = \

$$\begin{bmatrix} 2 & 4 \\\\ 1 & 3 \\end{bmatrix}$$

\\) and \\(b = \

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

\\).

add the matrices \\(a\\) and \\(b\\).

\\(\circ \

$$\begin{bmatrix} 2 & 4 \\\\ 1 & 3 \\end{bmatrix}$$

\\)

\\(\circ \

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

\\)

Explanation:

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<reasoning>

Identify the given matrices

Using the Matrix Addition knowledge point
\[
A =

$$\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$$

, \quad B =

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

\]

Perform element-wise addition

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

$$\begin{bmatrix} 2+0 & 4+0 \\ 1+0 & 3+0 \end{bmatrix}$$

=

$$\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$$

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

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

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

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"subject": "Mathematics",
"question_type": "Multiple Choice",
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"Mathematics",
"Algebra",
"Matrix Addition"
]
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Answer:

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<reasoning>

Identify the given matrices

Using the Matrix Addition knowledge point
\[
A =

$$\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$$

, \quad B =

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

\]

Perform element-wise addition

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

$$\begin{bmatrix} 2+0 & 4+0 \\ 1+0 & 3+0 \end{bmatrix}$$

=

$$\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$$

\]
</reasoning>

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

$$\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$$

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

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

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

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"Mathematics",
"Algebra",
"Matrix Addition"
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