To multiply matrices, the number of columns of the first matrix must equal the number of rows of the second matrix. The solution matrix will have the number of rows of the first matrix and the number of columns of the second matrix. To calculate each element of the solution matrix, multiply the corresponding elements in that row of the first matrix with that column of the second matrix and sum the products.

1. Ch.8.6_MatrixMultiplication.notebook March 05, 2012
Chapter 8.6
Matrix Multiplication
Before multiplying matrices, you need
to check the dimensions of each matrix
rows x columns
The number of COLUMNS of the first matrix
needs to match the number of ROWS of the
second matrix
rows x columns
A2x3B3x2
2x3 3x2
The solution matrix will have the # of ROWS from
the first matrix and the # of COLUMNS from the
second matrix
2x3 3x2
Solution matrix will be 2x2
To multiply, we use row­by­column multiplication
Multiply corresponding elements and add the
products
(2)(1) + (1)(0) + (3)(6)
21
AB = Row 1 Column 1 Row 1 Column 2
Row 2 Column 1 Row 2 Column 2

2. Ch.8.6_MatrixMultiplication.notebook March 05, 2012
Find BA

3. Ch.8.6_MatrixMultiplication.notebook March 05, 2012