Multiplication of Matrices Section 2.5 Multiplication of Matrices

Matrix Multiplication Size of the product: If A is a matrix of size m x n and B is a matrix of size n x p (note: the column size of A must equal the row size of B), then the product AB will be a matrix of size m x p. Ex. Matrix A size 3 x 2 and matrix B size 2 x 5 3 x 2 2 x 5 Must be the same AB will be a matrix size 3 x 5 Ex. Matrix A size 3 x 4 and matrix B size 3 x 4 3 x 4 3 x 4 Must be the same The product AB can’t be computed

For matrices A, B, and C, let AB = C. Then And so on…

Ex. Given matrices B and C find BC and CB.

Ex. Now lets do CB. Note: in general, for any two square matrices B and C

Identity Matrix Diagonal of 1’s The identity matrix of size n is given by Diagonal of 1’s In A = A and BIn = B where defined.

Matrix Equation Representation of a System of Linear Equations AX = B

Homework #1 P 98 1-6 all, 9 – 19odd , 21 – 24 all, 31- 34 all #2 P109 1 – 6 all, 7 – 23 eoo