Name
T E K S 2A.3.B
LESSON
4-5
Date
Class
Practice B
Matrix Inverses and Solving Systems
Determine whether the given matrices are inverses.
1.
5
4
0
1
0.2
0.8
0
1
2.
1 4
3
2
0.6 0.8
0.4 0.2
3.
2 3
1
1
1 3
1 2
Find the inverse of the matrix, if it is defined.
4.
1
0
4 1
5.
5 2
7 3
6.
8
4
5 3
7.
3 3
1
2
8.
4
4
5 4
9.
6 6
1 1
Write the matrix equation for the system, and solve.
10.
5
{ 4x3x 3y2y 9
11.
4y 8
{ 6x
5x 3y 5
12.
{ 5x4x 3y5y 130
13.
{ 6x5x 5y3y 48
Solve.
14. Keith paid $39 for 3 pounds of pistachios and 2 pounds of cashews.
Tracey paid $23 for 2 pounds of pistachios and 1 pound of cashews.
a. Write a system of equations. Let x the cost
of a pound of pistachios, and y the cost of a
pound of cashews.
b. Write the matrix equation and solve.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c04-5_pr_TX.indd 29
29
Holt Algebra 2
3/23/06 8:31:17 AM
Name
T E K S 2A.3.B
LESSON
4-5
Date
Class
Practice B
Matrix Inverses and Solving Systems
Determine whether the given matrices are inverses.
1.
5
4
0
1
0.2
0.8
0
1
2.
1 4
3
2
Yes
0.6 0.8
0.4 0.2
2 3
1
1
3.
Yes
1 3
1 2
Yes
Find the inverse of the matrix, if it is defined.
4.
1
0
4 1
5.
5 2
7 3
3 ⫺2
⫺7 5
1
0
4 1
7.
8
4
5 3
6.
3 3
1
2
8.
4
4
5 4
1
4
5 ⫺2
⫺__
4
6 6
1 1
9.
1 ⫺1
⫺__
3
2 ⫺1
⫺__
3
3
__
1 1
5 1
__
4
The inverse does not
exist.
Write the matrix equation for the system, and solve.
10.
5
{ 4x3x 3y2y 9
3 2 x
⫽
4 3 y
12.
11.
4y 8
{ 6x
5x 3y 5
⫺5 ; 3, ⫺7 ⫺9
⫺6 4
5 ⫺3
{ 5x4x 3y5y 130
13.
x
8 ⫽
; 2, 5 y
⫺5
{ 6x5x 5y3y 48
5 ⫺3
6 ⫺5
0 4 5 x
⫽
; 5, ⫺4 13
5 3 y
x
8 ⫽
; 4, 4 y
4
Solve.
14. Keith paid $39 for 3 pounds of pistachios and 2 pounds of cashews.
Tracey paid $23 for 2 pounds of pistachios and 1 pound of cashews.
a. Write a system of equations. Let x the cost
of a pound of pistachios, and y the cost of a
pound of cashews.
3 2 x
29 ;
⫽
23
2 1 y
pistachios: $7 per pound,
cashews: $9 per pound
b. Write the matrix equation and solve.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c04-5_pr_TX.indd 29
{
3x ⫹ 2y ⫽ 39
2x ⫹ y ⫽ 23
29
Holt Algebra 2
3/23/06 8:31:17 AM