How to Solve the Multiplication of Matrices
- 1). Create a 2 x 3 matrix labeled "A" and a 3 x 2 matrix labeled "B." Fill the top row of matrix A with the numbers 1, 0 and 3 and the bottom row with 0, -2 and 1. Fill the first column of matrix B with 0, 2, and 0 and the second column with 1, 3 and 0. Draw an empty 2 x 2 matrix labeled "AB" in which to record your solution.
- 2). Begin by multiplying the numbers in the first row of matrix A and the first column of matrix B, then adding them together. Show your work:
(1 * 0) + (0 * 2) + (3 * 0) = 0
Write the number "0" in the first (upper left) box of the solution matrix. - 3). Multiply the numbers in the second row of matrix A by the first column of matrix B and add them together. Show your work:
(0 * 0) + (-2 * 2) + (1 * 0) = -4
Write the answer, -4, in the solution matrix beneath the 0, which would place it in the second row, first column. - 4). Multiply the numbers in the first row of A by the second column of B and add them together. Show your work:
(1 * 1) + (0 * 3) + (3 * 0) = 1
Write the answer, 1, in the solution matrix, placing it in the first row, second column. - 5). Finish off by multiplying the second row of A by the second column of B and adding them together. Show your work
(0 * 1) + (-2 * 3) + (1 * 0) = -6
Write the answer, -6, in the solution matrix in the remaining box -- second row, second column. - 6). Check your work; make sure that your solution matrix has 0 and 1 in the top row and -4 and -6 on the bottom row.