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\\)

Explanation:

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<reasoning>

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
\[

$$\begin{aligned} &\text{Dimensions: } (3 \times 4) \times (1 \times 3)\\ &\text{Inner dimensions do not match: } 4 e 1 \implies \text{Impossible} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(B \times A\)</mcq-correct>
<mcq-option>(B) \(A \times B\)</mcq-option>
</answer>

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Answer:

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<reasoning>

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
\[

$$\begin{aligned} &\text{Dimensions: } (3 \times 4) \times (1 \times 3)\\ &\text{Inner dimensions do not match: } 4 e 1 \implies \text{Impossible} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(B \times A\)</mcq-correct>
<mcq-option>(B) \(A \times B\)</mcq-option>
</answer>

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