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How to Multiply Matrices in Problems

A matrix is a bracketed set of numbers. You define the size of a matrix in terms of the number of horizontal rows and vertical columns. For example, a 3 x 4 matrix would have three rows and four columns. To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second. For example, a 3 x 4 matrix could multiply to a 4 x 3 matrix but not to a 3 x 2 matrix.

Instructions

- 1
  Multiply matrices A and B where A is a 2 x 3 matrix with a top row containing 2, 4 and 3 and a bottom row containing 1, 5 and 0, and B is a 3 x 2 matrix with 4, 2 and 2 in the first column and 3, 1 and 6 in the second column. Create an empty answer matrix of the size 2 x 2.
- 2
  Multiply the digits of the first row of A by the numbers in the first column of B and add the answers: 2 * 4 + 4 * 2 + 3 * 2 = 8 + 8 + 6 = 22. Write 22 in the top left spot of the answer matrix.
- 3
  Multiply the digits in the first row of A by the second column of B, adding the results: 2 * 3 + 4 * 1 + 3 * 6 = 6 + 4 + 18 = 28. Write 28 in the top right space of the answer matrix.
- 4
  Multiply the digits in the second row of A by the first column of B: 1 * 4 + 5 * 2 + 0 * 2 = 4 + 10 + 0 = 14. Write 14 in the bottom left spot of the answer matrix.
- 5
  Multiply the digits in the second row of A by the second column of B: 1 * 3 + 5 * 1 + 0 * 6 = 3 + 5 + 0 = 8. Write 8 in the final (bottom right) spot of the answer matrix.

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