Multiply Matrices 1 Objectives To multiply matrices Warmup

Multiply Matrices 1. Objectives: To multiply matrices

Warm-up 1. How do you find the dimensions of a matrix? 2. We’ve learned how to add and subtract matrices and how to multiply by a scalar. How do you think we should multiply matrices?

Objective 1 You will be able to multiply matrices

Matrix Multiplication Multiplying two matrices is weird. Thank you, Arthur Cayley (1858). Arthur Cayley, 1850 ish

Matrix Multiplication Order: Must match Arthur Cayley, 1850 ish

Getting Rid of the Middle Man • When multiplying two matrices, the first thing you should do is find the order of the product!

Exercise 1 •

Exercise 2 a Multiply.

Exercise 2 b Multiply.

Exercise 2 c Multiply.

Exercise 2 d Multiply.

Exercise 2 d Multiply.

Exercise 2 d Multiply.

Exercise 2 d Multiply.

Exercise 2 d Multiply.

Exercise 2 d Multiply.

Matrix Multiplication Definition of Matrix Multiplication C o Row x l u m sense n This definition will make more once we do an application question.

Matrix Multiplication Definition of Matrix Multiplication C o l = RC + Ro + o l + o u + w m + w n RRo o w w x u m n

The Order of the Product So you might be asking why the number of columns of the first matrix must equal the number of rows in the second matrix. This is because we must multiply a row (in the first matrix) by a column (in the second matrix), and the number of elements must match. How many elements are there in any row in the first matrix? How many elements are there in any column in the second matrix?

Exercise 3 a Two softball teams submit equipment lists to their sponsors. Bats Balls Gloves Woman’s Team 12 45 15 Men’s Team 15 38 17 If a bat costs $21, a ball costs $4, and a glove costs $30, use matrices to find the total cost of equipment for each team.

Exercise 3 b The previous Exercise simplifies to the following matrix multiplication problem. Can you now see why matrix multiplication is so weird?

Exercise 4 •

Exercise 5 •

Properties of Matrix Multiplication • Associative Property of Matrix Multiplication Left Distributive Property Right Distributive Property Associative Property of Scalar Multiplication Remember: Remember There is no commutative property for matrix multiplication!

Identity Matrix • Identity Property of Matrix Multiplication

Identity Matrix •

Exercise 6 •

Exercise 7 •

Exercise 8 •

3. 6: Multiply Matrices 1. Objectives: To multiply matrices