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

The problem presents A and B and asks which statement is correct, but the provided answer options are missing. Despite that, we can independently compute the product AB to verify any candidate statement.

First, write the matrices:
A = [[2, -1], [-3, -4]] and B = [[-2, 0], [-1, 3]].

Compute AB using matrix multiplication: AB = A × B.
- Entry (1,1): (2)(-2) + (-1)(-1) = -4 + 1 = -3.
- Entry (1,2): (2)(0) + (-1)(3) = 0 + (-3) = -3.
So the first row of AB is [-3, -3].
- Entry (2,1): (-3)(-2) + (-4)(-1) = 6 + 4 = 10.
- Entry (2,2): (-3)(0) + (-4)(3) = 0 + (-12) = -12.
So the second row of AB is [10, -12].

Thus AB = [[-3, -3], [10, -12]].

Now compare with the statement given in the answer field: "c. AB = [[-3, -3], [10, -12]]". This matches exactly the computed product AB, confirming that, if that were the statement among the options, it would be correct.

Since the actual list of answer options is missing, we cannot assess the other potential choices or identify which option letter corresponds to AB. The essential calculation here is that AB equals [[-3, -3], [10, -12]], and the provided matrix for AB aligns with that result.

If you supply the full set of answer options, I can map AB to the correct choice letter and explain why the other options (if any) would be incorrect.

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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