4.1: Matrix OperationsObjectives: Students will be able to:• Add, subtract, and multiply a matrix by a scalar• Solve Matrix Equations• Use matrices to organize data

Matrix

A rectangular arrangement of numbers in rows and columns

Dimensions of a Matrix: # rows by # columns

2 X 3 (read 2 by 3)

701

436

Entries: the numbers in a matrix

Square Matrix: a matrix with the same # of rows and columns

What are the dimensions of the matrices below?

1. 2. 3.

32

41

10

7

1

265

305

712

Two matrices are equal if their dimensions are the same and the entries in corresponding positions are equal.

Are the following matrices equal?

1. and 2. and

44

12

17

425.

5.7

53

21

38

10

To add and subtract matrices, add or subtract corresponding entries:

Can only add and subtract if matrices have the same dimensions

Perform the indicated operations:1. 2. 3.

8

9

1

3

4

0

53

02

59

33

84

3179

Scalar Multiplication: multiply each entry of the matrix by the scalar

1.

2.

48

326

41

89

63

92

33

74

1

Solving Matrix Equations: Solve for x and y

1.

Method 1: Simplify inside parenthesis then multiply

Method 2: Multiply scalar then add

80

4848

61

24

21

084

x

y

Solve for x and y:

2118

90

11

5

45

2103

x

y

Properties of Matrix Operations: A, B and C are matrices, c is a scalar

1. Associative Property (regroup)

2. Commutative Property (change order)

3. Distributive Property of Addition

4. Distributive Property of Subtractions

(A+B)+C = A +(B+C)

A + B = B +A

c(A +B) = cA + cB

c(A- B) = cA- cB

Using Matrices to Organize Data:

Use matrices to organize the following data about insurance rates.

This year for 1 car, comprehensive, collision and basic insurance cost $612.15, $518.29 and $486.91. For 2 cars, comprehensive, collision and basic insurance cost $1150.32, $984.16, and $892.51.Next year for 1 car, comprehensive, collision and basic insurance will cost $616.28, $520.39, and $490.05. For 2 cars, comprehensive, collision and basic insurance will cost $1155.84, $987.72, and $895.13.

Use the matrices to write a matrix that shows the MONTHLY changes from this year to next.