Essential Questions

Monday, October 18 Essential Questions • How do I perform basic matrix operations?

1.8 Perform Basic Matrix Operations Adding and Subtracting Matrices To add or subtract two matrices, simply add or subtract _______________ elements. corresponding You can add or subtract matrices only if they have the same ____________. dimensions Adding Matrices Subtracting Matrices

1.8 Perform Basic Matrix Operations • The dimensions of are ________ and the dimensions of are _______. So, you _________ subtract the matrices. Add and subtract matrices Example 1 Perform the indicated operation, if possible. Solution 2 X 2 2 X 1 cannot

1.8 Perform Basic Matrix Operations Add and subtract matrices Example 1 Perform the indicated operation, if possible. Solution • The dimensions are __________. So, add the matrices. the same

1.8 Perform Basic Matrix Operations Multiply a matrix by a scalar Example 2 Perform the indicated operation, if possible.

1.8 Perform Basic Matrix Operations Checkpoint. Perform the indicated operation, if possible.

1.8 Perform Basic Matrix Operations Properties of Matrix Operations Let A, B, and C be matrices with the same dimensions, and let k be a scalar. Associative Property of Addition Commutative Property of Addition Distributive Property of Addition Distributive Property of Subtraction

1.8 Perform Basic Matrix Operations Solve a multi-step problem Example 3 Pet Stores Two pet stores sell both dogs and cats. Sales from each store for last month and this month are shown below. Last Month: Store 1 sold 42 dogs, 33 cats Store 2 sold 56 dogs, 21 cats This Month: Store 1 sold 36 dogs, 51 cats Store 2 sold 48 dogs, 37 cats Organize the data into matrices, then write and interpret a matrix giving the average monthly sales for the two month period. Solution • Organize the data into two 2 x 2 matrices. Last month (A) This month (B) dogs dogs cats cats Store 1 Store 1 Store 2 Store 2

1.8 Perform Basic Matrix Operations Solve a multi-step problem Example 3 Pet Stores Two pet stores sell both dogs and cats. Sales from each store for last month and this month are shown below. Last Month: Store 1 sold 42 dogs, 33 cats Store 2 sold 56 dogs, 21 cats This Month: Store 1 sold 36 dogs, 51 cats Store 2 sold 48 dogs, 37 cats Write a matrix for the average monthly sales by adding A and B and then multiplying the result by ½.

1.8 Perform Basic Matrix Operations Solve a multi-step problem Example 3 Pet Stores Two pet stores sell both dogs and cats. Sales from each store for last month and this month are shown below. Last Month: Store 1 sold 42 dogs, 33 cats Store 2 sold 56 dogs, 21 cats This Month: Store 1 sold 36 dogs, 51 cats Store 2 sold 48 dogs, 37 cats Interpret the matrix from Step 2. Store 1 sold an average of ____ dogs and ___ cats, while Store 2 sold an average of ___ dogs and ___ cats. 42 39 52 29

1.8 Perform Basic Matrix Operations Solve a matrix equation Example 4 Solve the matrix equation for x and y. Solution Simplify the left side of the equation. Write original equation. Add matrices inside parentheses. Perform scalar multiplication.

1.8 Perform Basic Matrix Operations Solve a matrix equation Example 4 Solve the matrix equation for x and y. Solution Equate corresponding elements and solve the two resulting equations. The solution is x = ____ and y = ____.

1.8 Perform Basic Matrix Operations Checkpoint. Complete the following exercise. • Solve the matrix equation for x and y.

1.8 Perform Basic Matrix Operations Pg. 45, 1.8 #1-23

Essential Questions