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

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

12 + -3 + 19 10

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

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 5 B is a 2 x 5 C is a 5 x 1 D is a 3 x 2

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

2) Find the product of the given matrices:

2) Find the product of the given matrices:

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

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.

Identity Matrix Find the product of I and A

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

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