multiply the matrices $a = \begin{bmatrix} 2 & -4 \\ 0 & 1 \\ 3 & 5 \end{bmatrix}$ and $b = \begin{bmatrix} 1 & 6 \\ 0 & 7 \end{bmatrix}$.

$\circ \begin{bmatrix} 2 & -16 \\ 0 & 7 \\ 3 & 53 \end{bmatrix}$
$\circ \begin{bmatrix} 2 & -16 & 0 \\ 13 & 3 & 53 \end{bmatrix}$

Question

multiply the matrices $a = \begin{bmatrix} 2 & -4 \\ 0 & 1 \\ 3 & 5 \end{bmatrix}$ and $b = \begin{bmatrix} 1 & 6 \\ 0 & 7 \end{bmatrix}$.

$\circ \begin{bmatrix} 2 & -16 \\ 0 & 7 \\ 3 & 53 \end{bmatrix}$
$\circ \begin{bmatrix} 2 & -16 & 0 \\ 13 & 3 & 53 \end{bmatrix}$

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 Dimensions", "Matrix Multiplication" ], "new_concepts": [], "current_concepts": [ "Matrix Dimensions", "Matrix Multiplication" ] } ## Check matrix dimensions Using the *Matrix Dimensions* knowledge point $$ \begin{aligned} &\text{Dimension of } A: 3 \times 2\ &\text{Dimension of } B: 2 \times 2\ &\text{Inner dimensions match: } 2 = 2\ &\text{Resulting dimension of } AB: 3 \times 2 \end{aligned} $$ ## Compute the product matrix elements Using the *Matrix Multiplication* knowledge point $$ \begin{aligned} C_{11} &= 2(1) + (-4)(0) = 2\ C_{12} &= 2(6) + (-4)(7) = 12 - 28 = -16\ C_{21} &= 0(1) + 1(0) = 0\ C_{22} &= 0(6) + 1(7) = 7\ C_{31} &= 3(1) + 5(0) = 3\ C_{32} &= 3(6) + 5(7) = 18 + 35 = 53 \end{aligned} $$ ## Construct the final product matrix Using the *Matrix Multiplication* knowledge point $$ AB = \begin{bmatrix} 2 & -16 \ 0 & 7 \ 3 & 53 \end{bmatrix} $$

$\begin{bmatrix} 2 & -16 \ 0 & 7 \ 3 & 53 \end{bmatrix}$

$\begin{bmatrix} 2 & -16 & 0 \ 13 & 3 & 53 \end{bmatrix}$

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

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QUESTION IMAGE

Question

Explanation:

Check matrix dimensions

Compute the product matrix elements

Construct the final product matrix

Answer: