1 A = [[3, - 2], [1, 4]] and B = [[0, - 1], [3, 2]] what is AB? (1 point) If
A = [[3, -2], [1, 4]] and B = [[0, -1], [3, 2]], the product AB can be calculated by multiplying corresponding elements of A and B and adding them together.
To find the element in the first row and first column of AB, we multiply the first element in the first row of A (3) with the first element in the first column of B (0), and multiply the second element in the first row of A (-2) with the second element in the first column of B (3), then add them together:
AB[0][0] = (3*0) + (-2*3) = 0 - 6 = -6
To find the element in the first row and second column of AB, we multiply the first element in the first row of A (3) with the first element in the second column of B (-1), and multiply the second element in the first row of A (-2) with the second element in the second column of B (2), then add them together:
AB[0][1] = (3*-1) + (-2*2) = -3 - 4 = -7
To find the element in the second row and first column of AB, we multiply the first element in the second row of A (1) with the first element in the first column of B (0), and multiply the second element in the second row of A (4) with the second element in the first column of B (3), then add them together:
AB[1][0] = (1*0) + (4*3) = 0 + 12 = 12
To find the element in the second row and second column of AB, we multiply the first element in the second row of A (1) with the first element in the second column of B (-1), and multiply the second element in the second row of A (4) with the second element in the second column of B (2), then add them together:
AB[1][1] = (1*-1) + (4*2) = -1 + 8 = 7
Therefore, AB = [[-6, -7], [12, 7]].