question 18 points 2

$a = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 0 & -2 & -1 & 2 \end{bmatrix}$, $b = \begin{bmatrix} 1 & 4 & 3 \end{bmatrix}$, and $c = \begin{bmatrix} 2 & 4 \\ 6 & 8 \end{bmatrix}$. for the given matrices, which of the following is possible?

* $b \times a$
* $a \times b$

Question

question 18 points 2

$a = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 0 & -2 & -1 & 2 \end{bmatrix}$, $b = \begin{bmatrix} 1 & 4 & 3 \end{bmatrix}$, and $c = \begin{bmatrix} 2 & 4 \\ 6 & 8 \end{bmatrix}$. for the given matrices, which of the following is possible?

* $b \times a$
* $a \times b$

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" ] } ## Determine the dimensions of each matrix Using the *Matrix Dimensions* knowledge point $$ \begin{aligned} &\text{Matrix } A \text{ has } 3 \text{ rows and } 4 \text{ columns} \implies 3 \times 4\ &\text{Matrix } B \text{ has } 1 \text{ row and } 3 \text{ columns} \implies 1 \times 3\ &\text{Matrix } C \text{ has } 2 \text{ rows and } 2 \text{ columns} \implies 2 \times 2 \end{aligned} $$ ## Check compatibility for B x A Using the *Matrix Multiplication* knowledge point $$ \begin{aligned} &\text{Dimensions: } (1 \times 3) \times (3 \times 4)\ &\text{Inner dimensions match: } 3 = 3\ &\text{Resulting dimension: } 1 \times 4 \implies \text{Possible} \end{aligned} $$ ## Check compatibility for A x B Using the *Matrix Multiplication* knowledge point $$ \begin{aligned} &\text{Dimensions: } (3 \times 4) \times (1 \times 3)\ &\text{Inner dimensions do not match: } 4 e 1 \implies \text{Impossible} \end{aligned} $$

(A) $B \times A$

(B) $A \times B$

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

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Question

Explanation:

Determine the dimensions of each matrix

Check compatibility for B x A

Check compatibility for A x B

Answer: