lesson 7 matrices ncscos obj.: 1.02; 3.01; 3.02 objectives: tlw add and subtract matrices tlw...
TRANSCRIPT
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: