How do I perform basic matrix operations 1

• 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 corresponding elements. ________ You can add or subtract matrices only if they have the dimensions same ______. Adding Matrices Subtracting Matrices

1. 8 Perform Basic Matrix Operations Example 1 Add and subtract matrices Perform the indicated operation, if possible. Solution a. The dimensions of 2 X 2 and the are ____ 2 X 1 So, you _____ cannot are _______. subtract the matrices.

1. 8 Perform Basic Matrix Operations Example 1 Add and subtract matrices Perform the indicated operation, if possible. Solution the same So, add the matrices. b. The dimensions are _____.

1. 8 Perform Basic Matrix Operations Example 2 Multiply a matrix by a scalar 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 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 Subtraction

1. 8 Perform Basic Matrix Operations Example 3 Solve a multi-step problem Pet Stores Two pet stores sell both dogs and cats. Sales from each store for last month and this month are shown below. Last Store 1 sold 42 dogs, 33 cats Month: Store 2 sold 56 dogs, 21 cats This Store 1 sold 36 dogs, 51 cats Month: Store 2 sold 48 dogs, 37 cats Organize Solutionthe data into matrices, then write and interpret a matrix giving the average monthly sales 2 for two month period. 1. Organize the data into two x 2 the matrices. Last month (A) dogs cats This month (B) dogs cats Store 1 Store 2

1. 8 Perform Basic Matrix Operations Example 3 Solve a multi-step problem Pet Stores Two pet stores sell both dogs and cats. Sales from each store for last month and this month are shown below. Last Store 1 sold 42 dogs, 33 cats Month: Store 2 sold 56 dogs, 21 cats This Store 1 sold 36 dogs, 51 cats Month: 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 Example 3 Solve a multi-step problem Pet Stores Two pet stores sell both dogs and cats. Sales from each store for last month and this month are shown below. Last Store 1 sold 42 dogs, 33 cats Month: Store 2 sold 56 dogs, 21 cats This Store 1 sold 36 dogs, 51 cats Month: Store 2 sold 48 dogs, 37 cats Interpret the matrix from Step 2. Store 1 sold an average of 42 cats, while Store 2 sold an average of ____ 39 dogs and ___ 52 29 cats. dogs and ___

1. 8 Perform Basic Matrix Operations Example 4 Solve a matrix equation 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 Example 4 Solve a matrix equation 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. 3. Solve the matrix equation for x and y.

1. 8 Perform Basic Matrix Operations Checkpoint. Complete the following exercise. 3. Solve the matrix equation for x and y.

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