In Exercises 1-4, verify that B is the inverse of A by showing that AB = BA = 1. 1. A = 2. A = 3. A = 4. A = 7 4 5 3 3 10 2 10 B = B = -1 -2 11 1 3-15 0-1 5 00 210 34 1 " 3-4 7 1 -1 3 -5 B = -.2 B = -2 013 554 5-4 In Exercises 5-8, use the appropriate inverse matrix from Exercises 1-4 to solve the given system of linear equations. 5. 3x1 + 10x2= 6 2x1 + 10x2 = 9 7. x2 + 3x3 = 4 5x1 + 5x2 + 4x3 = 2 x₁ + x₂ + x3 = 2 9. A = 6. 7x1 + 4x2 = 5 5x1 + 3x2 = 2 3 2 1 8. In Exercises 9-12, verify that the given matrix A does not have an inverse. [Hint: One of AB= I or BA = I leads to an easy contradiction.] 00 X1 = 2 -2x1 + x₂ = 3 5x₁4x2 + x3 = 2 10. A = 042 017 039

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
100%
Linear algebra: please solve q3 and 7 correctly and handwritten
In Exercises 1-4, verify that B is the inverse of A by
showing that AB = BA = 1.
1. A =
2. A =
3. A =
4. A =
7 4
5 3
3 10
2 10
B =
00
210
34 1
B =
-1 -2 11
1 3 -15
0-1
5
"
3-4
7
-5
B =
1 -1
3
-.2
B =
-2
013
554
5-4
In Exercises 5-8, use the appropriate inverse matrix
from Exercises 1-4 to solve the given system of linear
equations.
5. 3x1 + 10x2=6
2x1 + 10x2 = 9
7.
x2 + 3x3 = 4
5x1 + 5x2 + 4x3 = 2
x₁ + x₂ + x3 = 2
9. A =
6. 7x1 + 4x2 = 5
5x1 + 3x2= 2
3 2 1
8.
In Exercises 9-12, verify that the given matrix A does
not have an inverse. [Hint: One of AB= I or BA = I
leads to an easy contradiction.]
00
X1
= 2
-2x1 + x₂
= 3
5x₁4x2 + x3 = 2
10. A =
042
017
0 39
Transcribed Image Text:In Exercises 1-4, verify that B is the inverse of A by showing that AB = BA = 1. 1. A = 2. A = 3. A = 4. A = 7 4 5 3 3 10 2 10 B = 00 210 34 1 B = -1 -2 11 1 3 -15 0-1 5 " 3-4 7 -5 B = 1 -1 3 -.2 B = -2 013 554 5-4 In Exercises 5-8, use the appropriate inverse matrix from Exercises 1-4 to solve the given system of linear equations. 5. 3x1 + 10x2=6 2x1 + 10x2 = 9 7. x2 + 3x3 = 4 5x1 + 5x2 + 4x3 = 2 x₁ + x₂ + x3 = 2 9. A = 6. 7x1 + 4x2 = 5 5x1 + 3x2= 2 3 2 1 8. In Exercises 9-12, verify that the given matrix A does not have an inverse. [Hint: One of AB= I or BA = I leads to an easy contradiction.] 00 X1 = 2 -2x1 + x₂ = 3 5x₁4x2 + x3 = 2 10. A = 042 017 0 39
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,