Let A=[2−1−3−4] A = \begin{bmatrix} 2 & -1 \ -3 & -4 \end{bmatrix}, B=[−20−13] B = \begin{bmatrix} -2 & 0 \ -1 & 3 \end{bmatrix}.Which of the following statements is correct?

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BlackTom AI · Accepted Answer

The question provides matrices A and B and asks which statement is correct, but the list of answer options is not present. To still engage with the content, I will verify the given candidate statement and show how to assess such options.
First, identify the matrix A from the prompt: A = [[2, -1], [-3, -4]]. To check a scalar multiple, multiply each entry of A by the scalar in question.
Second, consider the proposed expression: -3A. Compute each entry by multiplying A's corresponding entry by -3:
- Top-left: 2 * (-3) = -6
- Top-right: (-1) * (-3) = 3
- Bottom-left: (-3) * (-3) = 9
- Bottom-right: (-4) * (-3) = 12
Thus, -3A = [[-6, 3], [9, 12]].
Now compare this result to the statement given: 'c. -3A = [[-6, 3], [9, 12]]'. The numerical result matches exactly, confirming that, at least for this specific claim, the equality holds true.
If there were other statements to compare, you would apply the same approach to each: compute the scalar multiplication on A (or B, if involved) and verify whether the resulting matrix matches the stated expression. Discrepancies would reveal incorrect options, while a precise match confirms correctness.
Note on completeness: since no other answer options are provided in the data, there is no basis here to discuss potential alternatives or distractors. In a typical multiple-choice setup, you would examine each option for consistency with standard matrix operations (associativity, distributivity, scalar multiplication, and the definition of the identity with respect to matrix scaling).

ETC2410 - ETC5241 - BEX2410 - S2 2025 Tutorial 2: Part A Quiz

Let A=[2−1−3−4] A = \begin{bmatrix} 2 & -1 \\ -3 & -4 \end{bmatrix}, B=[−20−13] B = \begin{bmatrix} -2 & 0 \\ -1 & 3 \end{bmatrix}.Which of the following statements is correct?

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ETC2410 - ETC5241 - BEX2410 - S2 2025 Tutorial 2: Part A Quiz

Let A=[2−1−3−4] A = \begin{bmatrix} 2 & -1 \\ -3 & -4 \end{bmatrix}, B=[−20−13] B = \begin{bmatrix} -2 & 0 \\ -1 & 3 \end{bmatrix}.Which of the following statements is correct?

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Let \( A = \begin{bmatrix} 2 & -1 \\ -3 & -4 \end{bmatrix}\), \( B = \begin{bmatrix} -2 & 0 \\ -1 & 3 \end{bmatrix}\).Which of the following statements is correct?

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