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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BlackTom AI · Accepted Answer

We start by identifying the matrices given in the problem: A = [[2, -1], [-3, -4]] and B = [[-2, 0], [-1, 3]]. The question asks which statement is correct, and the provided answer option is c. $ -3A = \begin{bmatrix} -6 & 3 \ 9 & 12 \end{bmatrix} $.

To verify this, perform scalar multiplication of A by -3: multiply each entry of A by -3.
- Top-left: -3 * 2 = -6
- Top-right: -3 * (-1) = 3
- Bottom-left: -3 * (-3) = 9
- Bottom-right: -3 * (-4) = 12
Thus, -3A = [[-6, 3], [9, 12]], which matches the given option.

If one were to consider other possible statements (not provided here), we would similarly check them by applying the appropriate matrix operations and comparing results. Since only option c is presented, we confirm that this computation is correct by direct entrywise multiplication. This also illustrates the general rule that multiplying a matrix by a scalar scales every element by that scalar.

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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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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