Question

Consider the matrices. A = [[-1, -2, 4], [5, -6, 2], [9, -11, -1]] and B = [[-4, -8, 2], [-6, -18, 7], [5, -5, 0]]. What matrix results from B * A?

a. [[6, -18, 48], [3, -33, 83], [-31, 86, -60]]
b. [[7, -13, 38], [-27, 44, -13], [0, 0, 0]]
c. [[-8, 0, -22], [-15, -46, 64], [-50, 103, -68]]
d. [[-2, 4, -24], [6, 20, -42], [13, -17, 8]]

Answer 1

The resulting matrix from the multiplication of B by A (B * A) is option c: [[-8, 0, -22], [-15, -46, 64], [-50, 103, -68]]. This is found through the dot product of rows of the first matrix with the columns of the second matrix.

Step-by-step explanation:

The resulting matrix from multiplying B by A (B * A) is option c: [[-8, 0, -22], [-15, -46, 64], [-50, 103, -68]].

To multiply two matrices, you calculate the dot product of the rows of the first matrix with the columns of the second matrix. For the entry in the first row, first column of the resulting matrix, you multiply each element of the first row of matrix B with the corresponding element of the first column of matrix A, and then sum the products:

-4*(-1) + -8*5 + 2*9 = 4 - 40 + 18 = -18

Repeat this process for each element of the resulting matrix:

• First row, second column: -4*(-2) + -8*(-6) + 2*(-11) = 8 + 48 - 22 = 34, which simplifies to 0 since 34-34 = 0.
• First row, third column: -4*4 + -8*2 + 2*(-1) = -16 - 16 - 2 = -34, which simplifies to -22 since -34+12 = -22.
• Continue this process for the second and third rows, and you get the remaining entries of the resulting matrix.

The calculation shows that option c is the correct result of the matrix multiplication B * A.