1. Multiplying Matrices Lesson 4.2

2. Definition of Multiplying Matrices The product of two matrices A and B is defined provided the number of columns in A is equal to the number of rows in B. mxn nxp mxp

3. Example 1: Describing Matrix Products A) A = 3x4 B = 2x4 B) A = 3x4 B = 4x3

4. Example 2: Find the Product of Two Matrices A)B)

5. Properties of Matrix Multiplication Let A, B and C be matrices and let c be a scalar. Associative Property of Matrix Multiplication: A(BC) = (AB)C Left Distributive: A(B + C) =AB + AC Right Distributive: (A + B)C = AC + BC Associative Property of Scalar Multiplication: c(AB) = (cA)B = A(cB)

6. Example 3: Using Matrix Operations If A = B=C= Simplify the expression A(B + C).

7. Example 4: Using Matrices to Calculate Total Cost Tim wants 4 notebooks, 5 pens, and 10 pencils for the new school year. Leslie wants 5 notebooks, 8 pens, and 8 pencils. Each notebook is $4, each pen is $2 and each pencil is $1. Use matrix multiplication to find the total cost for each person.