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 restating the problem: Given A = [[2, -1], [-3, -4]] and B = [[-2, 0], [-1, 3]], determine which statement about AB is correct. The answer provided is 'b. AB = [[-3, -3], [10, -12]]', but no other options are listed to compare against.

To verify, compute the product AB step by step. First, multiply A by B using standard matrix multiplication:
- The entry in the first row, first column: (2)(-2) + (-1)(-1) = -4 + 1 = -3.
- The entry in the first row, second column: (2)(0) + (-1)(3) = 0 - 3 = -3.
Thus, the first row of AB is [-3, -3].

- The entry in the second row, first column: (-3)(-2) + (-4)(-1) = 6 + 4 = 10.
- The entry in the second row, second column: (-3)(0) + (-4)(3) = 0 - 12 = -12.
Thus, the second row of AB is [10, -12].

So AB = [[-3, -3], [10, -12]]. The provided statement in option b matches this computed product exactly.

Since the computed product aligns with the given option b, that statement is correct. If there were more options, we would compare AB to each one, but with the information available, AB coincides with the matrix listed in option b, confirming its correctness.

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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