• How do I perform basic matrix operations?

1.8 Perform Basic Matrix Operations

Adding and Subtracting MatricesTo add or subtract two matrices, simply add or subtract _______________ elements. correspondingYou can add or subtract matrices only if they have the same ____________.dimensions

Adding Matrices

hgfe

dcba

hdgcfbea

Subtracting Matrices

hgfe

dcba

hdgcfbea

1.8 Perform Basic Matrix Operations

Example 1 Add and subtract matricesAdd and subtract matrices

Perform the indicated operation, if possible.Perform the indicated operation, if possible.

23

3126 .a

519241

673012

.b

Solution

a. The dimensions of are ________ and the

3126

dimensions of are _______. So, you _________

23

subtract the matrices.

2 X 2

2 X 1 cannot

1.8 Perform Basic Matrix Operations

Example 1 Add and subtract matricesAdd and subtract matrices

Perform the indicated operation, if possible.Perform the indicated operation, if possible.

23

3126 .a

519241

673012

.b

Solutionb. The dimensions are __________. So, add the matrices.the same

_________________519241

673012 12 41

20 93 17 56

________

1 32 128 11

1.8 Perform Basic Matrix Operations

______________461

720 3 a. 03 23 73 13 63 43

Example 2 Multiply a matrix by a scalarMultiply a matrix by a scalar

Perform the indicated operation, if possible.Perform the indicated operation, if possible.

___________0 6 213 18 12

____________53

01 2 b. 12 02 32 52

______

2 06 10

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

1703

5126 1.

2 2 2 2

9 2

8 4

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

0692

42313 2.

3 69 126 27 18 0

1.8 Perform Basic Matrix Operations

Properties of Matrix OperationsLet A, B, and C be matrices with the same dimensions, and let k be a scalar. Associative Property of Addition

__________ CBA CBA Commutative Property of Addition

______BA AB Distributive Property of Addition

__________ BAk kBkADistributive Property of Subtraction

__________ BAk kBkA

1.8 Perform Basic Matrix Operations

Example 3 Solve a multi-step problemSolve a multi-step problemPet Stores Pet Stores Two pet stores sell both dogs and Two pet stores sell both dogs and cats. Sales from each store for last month and cats. Sales from each store for last month and this month are shown below.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.Solution1. Organize the data into two 2 x 2 matrices.

Last month (A)

_________

dogs cats

Store 1

Store 2

This month (B)

_________

dogs cats

Store 1

Store 242 3356 21

36 5148 37

1.8 Perform Basic Matrix Operations

Example 3 Solve a multi-step problemSolve a multi-step problemPet Stores Pet Stores Two pet stores sell both dogs and Two pet stores sell both dogs and cats. Sales from each store for last month and cats. Sales from each store for last month and this month are shown below.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.

______________2

1

2

1BA

42 3356 21

36 5148 37

_______2

1 78 84104 58

_______39 4252 29

1.8 Perform Basic Matrix Operations

Example 3 Solve a multi-step problemSolve a multi-step problemPet Stores Pet Stores Two pet stores sell both dogs and Two pet stores sell both dogs and cats. Sales from each store for last month and cats. Sales from each store for last month and this month are shown below.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.39 42 52

29

1.8 Perform Basic Matrix Operations

Example 4 Solve a matrix equationSolve a matrix equation

Solve the matrix equation for Solve the matrix equation for xx and and y y..

08

88

22

31

60

13 4

y

x

SolutionSimplify the left side of the equation.

08

88

22

31

60

13 4

y

x Write original equation.

08

88

______________ 4 13 x 2

2 y26 Add matrices inside parentheses.

08

88

______________ 412 x 8

8 y824 Perform scalar multiplication.

1.8 Perform Basic Matrix Operations

Example 4 Solve a matrix equationSolve a matrix equation

Solve the matrix equation for Solve the matrix equation for xx and and y y..

08

88

22

31

60

13 4

y

x

SolutionEquate corresponding elements and solve the two resulting equations.

8_______ 412 x 0_______ y824 _______ x12 12___x 1

_______ y8 24___y 3

The solution is x = ____ and y = ____.1 3

1.8 Perform Basic Matrix OperationsCheckpoint. Complete the following exercise.Checkpoint. Complete the following exercise.

68

124

45

61

71

232

y

x

68

124

2

3. Solve the matrix equation for x and y.

2 62 x15 y 3

68

124

4 124 x210 y 6

1.8 Perform Basic Matrix OperationsCheckpoint. Complete the following exercise.Checkpoint. Complete the following exercise.

3. Solve the matrix equation for x and y.

68

124

4 124 x210 y 6

12124 x 8210 y

244 x6x

1010 y1y

1.8 Perform Basic Matrix Operations

Pg. 45, 1.8 #1-23