1. Matrix Multiplication
Section 4-3
Algebra II CP
Mrs. Sweet

2. Row by Column Multiplication:
The product of matrix A and B is found by multiplying the of matrix A by the of matrix B.
Then the final products.
row
column
adding

3. 12 + -3 + 19 10

4. Matrices can be multiplied only when the number of for the left matrix
matches the number of of the right matrix.
columns
rows
If A has dimensions n x p and B has dimensions
p x q then AB will have dimensions:
n x q

5. A is a 3 x 5 B is a 2 x 5 C is a 5 x 1 D is a 3 x 2
Examples:
1) Given the dimensions of the following matrices determine if they can be multiplied if so find the dimensions of their product:
A is a 3 x B is a 2 x C is a 5 x D is a 3 x 2

6. Is matrix multiplication Commutative?
Give an example:
Is matrix multiplication Associastive?
Give an example:

7. 2) Find the product of the given matrices:

8. 2) Find the product of the given matrices:

9. 6 2 5 -4 8 1 2 =
0 3 22 50 12 =
-12 3

10. An ounce of ground beef has about 60 calories
An ounce of ground beef has about 60 calories. A single French fry has about 11 calories. An ounce of yogurt has about 40 calories.
1) If you eat a quarter pound of beef, 20 French fries, and 4 ounces of yogurt, how many calories will you have consumed?
2) Write the question as a matrix multiplication.

11. Identity Matrix
Find the product of I and A

12. diagonal An Identity Matrix is an n x n matrix whose main from
upper left to lower right has all elements 1 while all other elements are 0.
diagonal

13. What would be the identity matrix for a 3 x 3 matrix?
1 0 0
0 1 0
0 0 1