Lesson 7 Matrices

NCSCOS Obj.: 1.02; 3.01; 3.02Objectives:

TLW add and subtract MatricesTLW Multiply a Matrix by a

ScalarTLW identify and analyze data

in a matrix

MATRIX: A rectangular arrangement of numbers in rows and columns.

The DIMENSION of a matrix is the number of the rows and columns.

The ENTRIES are the numbers in the matrix.

502

126rows

columns

The dimension of this matrix is a 2 x 3.

67237

89511

36402

3410

200

318 0759

20

11

6

0

7

9

3 x 3

3 x 5

2 x 2 4 x 1

1 x 4

(or square matrix)

(Also called a row matrix)

(or square matrix)

(Also called a column matrix)

To add two matrices, they must have the same order. To add, you simply add corresponding entries.

34

03

12

70

43

35

)3(740

0433

13)2(5

44

40

23

9245

3108

2335

2571

)1(8 70 51 23

55 34 32 )2(9 =

= 7 7 4 5

0 7 5 7

To subtract two matrices, they must have the same order. You simply subtract corresponding entries.

232

451

704

831

605

429

2833)2(1

)4(65015

740249

603

1054

325

724

113

810

051

708

342

=

5-2

-4-1 3-8

8-3 0-(-1) -7-1

1-(-4)

2-0

0-7

=

2 -5 -5

5 1 -8

5 3 -7

In matrix algebra, a real number is often called a SCALAR. To multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar.

14

024

416

08

)1(4)4(4

)0(4)2(4

86

54

30

212

)8(360

52412

-2

6

-3 3

-2(-3)

-5

-2(6) -2(-5)

-2(3) 6 -6

-12 10

State the dimensions of the matrix. Then identify the position of the circled element in the matrix.

This matrix has 3 rows and 1 column.

Answer: It is a 3-by-1 matrix. The circled element is the second row and the first column.

State the dimensions of the matrix. Then identify the position of the circled element in the matrix.

This matrix has 3 rows and 4 columns.

Answer: It is a 3-by-4 matrix. The circled element is the first row and the fourth column.

Answer: 1 by 2; first row, first column

Answer: 2 by 4; second row, third column

State the dimensions of each matrix. Then identify the position of the circled element in the matrix.

a.

b.

Find the sum. If the sum does not exist, write impossible.

Definition of matrix addition

=

Answer: = Simplify.

Answer: It is impossible to add these matrices.

Find the sum. If the sum does not exist, write impossible.

Since the first matrix is a 2 by 2 matrix and the second matrix is a 3 by 3 matrix, the matrices do not have the same dimensions.

Find the sum. If the sum does not exist, write impossible.

a.

b.

Answer: impossible

Answer:

College Football The Division 1-A current football coaches with the five best overall records as of 2000 are listed below.

Overall Record Bowl Record

Coach Won Lost Tied Coach Won Lost Tied

Joe Paterno 322 90 3 Joe Paterno 20 9 1

Bobby Bowden 315 87 4 Bobby Bowden 17 6 1

Lou Holtz 224 110 7 Lou Holtz 11 8 2

Jackie Sherrill 172 93 4 Jackie Sherrill 8 6 0

Ken Hatfield 147 104 4 Ken Hatfield 4 6 0

Use subtraction of matrices to determine the regular season records of these coaches.

Answer: Regular Season Record

Coach Won Lost Tied

Joe Paterno 302 81 2

Bobby Bowden 298 81 3

Lou Holtz 213 102 5

Jackie Sherrill 164 87 4

Ken Hatfield 143 98 4

Four performing theaters have seating capacities listed below.

Overall Seating Capacity Number of Seats in the Balcony

TheaterLeft

SectionMiddle Section

Right Section

TheaterLeft

Section Middle Section

Right Section

King Theater 1065 640 1065

King Theater 385 180 385

Falcon Theater 840 620 840

Falcon Theater 210 190 210

Emerald Theater 615 550 615

Emerald Theater 175 140 175

Daisy Theater 530 410 530

Daisy Theater 160 120 160

Use subtraction of matrices to find the seating capacities on the main floors of the theaters.

Answer: Number of Seats on the Main Floor

TheaterLeft

SectionMiddle Section

Right Section

King Theater 680 460 680

Falcon Theater 630 430 630

Emerald Theater 440 410 440

Daisy Theater 370 290 370

Substitution

Definition of scalar multiplication

Simplify.Answer:

Answer: