question 27 points 1

what is $\begin{bmatrix} 2 & -3 \\ -4 & 2 \end{bmatrix} + \begin{bmatrix} -1 & -5 \\ 3 & -2 \end{bmatrix}$?

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

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

Question

question 27 points 1

what is $\begin{bmatrix} 2 & -3 \\ -4 & 2 \end{bmatrix} + \begin{bmatrix} -1 & -5 \\ 3 & -2 \end{bmatrix}$?

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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Matrix Addition" ], "new_concepts": [], "current_concepts": [ "Matrix Addition", "Matrix Dimensions" ] } ## 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 $$ \begin{aligned} A + B &= \begin{bmatrix} 2 + (-1) & -3 + (-5) \ -4 + 3 & 2 + (-2) \end{bmatrix}\ &= \begin{bmatrix} 1 & -8 \ -1 & 0 \end{bmatrix} \end{aligned} $$

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

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

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Matrix Addition" ] }

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Explanation:

Identify the dimensions of the matrices

Perform element-wise addition

Answer: