Question

question 27 points 1

what is \\(\

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

+ \

$$\begin{bmatrix} -1 & -5 \\\\ 3 & -2 \\end{bmatrix}$$

\\)?

\\(\circ \

$$\begin{bmatrix} 1 & -8 \\\\ -1 & 0 \\end{bmatrix}$$

\\)

\\(\circ \

$$\begin{bmatrix} -1 & 5 \\\\ 1 & -3 \\end{bmatrix}$$

\\)

Explanation:

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<reasoning>

Identify the dimensions of the matrices

Using the Matrix Addition knowledge point
\[

$$\begin{aligned} &A = \begin{bmatrix} 2 & -3 \\ -4 & 2 \end{bmatrix} \in \mathbb{R}^{2 \times 2}\\ &B = \begin{bmatrix} -1 & -5 \\ 3 & -2 \end{bmatrix} \in \mathbb{R}^{2 \times 2} \end{aligned}$$

\]

Perform element-wise addition

Using the Matrix Addition knowledge point
\[

$$\begin{aligned} A + B &= \begin{bmatrix} 2 + (-1) & -3 + (-5) \\ -4 + 3 & 2 + (-2) \end{bmatrix}\\ &= \begin{bmatrix} 1 & -8 \\ -1 & 0 \end{bmatrix} \end{aligned}$$

\]
</reasoning>

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

$$\begin{bmatrix} 1 & -8 \\ -1 & 0 \end{bmatrix}$$

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

$$\begin{bmatrix} -1 & 5 \\ 1 & -3 \end{bmatrix}$$

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

<post_analysis>
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"subject": "Mathematics",
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"Mathematics",
"Algebra",
"Matrix Addition"
]
}
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Answer:

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<reasoning>

Identify the dimensions of the matrices

Using the Matrix Addition knowledge point
\[

$$\begin{aligned} &A = \begin{bmatrix} 2 & -3 \\ -4 & 2 \end{bmatrix} \in \mathbb{R}^{2 \times 2}\\ &B = \begin{bmatrix} -1 & -5 \\ 3 & -2 \end{bmatrix} \in \mathbb{R}^{2 \times 2} \end{aligned}$$

\]

Perform element-wise addition

Using the Matrix Addition knowledge point
\[

$$\begin{aligned} A + B &= \begin{bmatrix} 2 + (-1) & -3 + (-5) \\ -4 + 3 & 2 + (-2) \end{bmatrix}\\ &= \begin{bmatrix} 1 & -8 \\ -1 & 0 \end{bmatrix} \end{aligned}$$

\]
</reasoning>

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

$$\begin{bmatrix} 1 & -8 \\ -1 & 0 \end{bmatrix}$$

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

$$\begin{bmatrix} -1 & 5 \\ 1 & -3 \end{bmatrix}$$

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

<post_analysis>
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"Mathematics",
"Algebra",
"Matrix Addition"
]
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