1. Multiplication of Matrices
Section 2.5
Multiplication of Matrices

2. 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 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 x 4
Must be the same
The product AB can’t be computed

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

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

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

6. 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.

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

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