solve each set of equations by the method of finding the inverse of the coefficient matrix. Hint: See Example 3. y + z = 4 2x + y - z = -1 3x + 2y + 2z
solve each set of equations by the method of finding the inverse of the coefficient matrix. Hint: See Example 3. y + z = 4 2x + y - z = -1 3x + 2y + 2z
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![solve each set of equations by the method of finding the inverse of
the coefficient matrix. Hint: See Example 3.
y + z =
4
2x + y
z = -1
3x + 2y + 2z =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b6d687b-9b3f-47af-8b4d-c251df44093c%2Fc6f11126-7f42-4d8b-8c56-5ac83aff625a%2Ft5o5zcs_processed.png&w=3840&q=75)
Transcribed Image Text:solve each set of equations by the method of finding the inverse of
the coefficient matrix. Hint: See Example 3.
y + z =
4
2x + y
z = -1
3x + 2y + 2z =
![• Example 3. For the matrix M of the coefficients in equations (6.7) or (6.9), find M-1.
1
0 -1
M = -2
3
1
-3
2
We find det M = 3. The cofactors of the elements are:
3 0
= 6,
-3 2
-2 0
= 4,
-2
1st row :
3
= 3.
1
2
1
-3
1
1
1
2nd
= 3,
= 3,
= 3.
-3
row :
-3
2
2
|0
1 0
= 3.
-2 3
-1
1
-
3rd row :
- 3,
2,
-2
Then
6 4 3
C =
1
CT
det M
6 3 3
1
4 3 2
3
3 3 3
3 3 3
so M-1 -
= -
3 2 3
Now we can use M-1 to solve equations (6.9). By (6.12), the solution is given by
the column matrix r = M-'k, so we have
6 3 3
1
4 3 2
3
3 3 3,
-10
or x = 1, y = 1, z = -4. (See Problem 12.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b6d687b-9b3f-47af-8b4d-c251df44093c%2Fc6f11126-7f42-4d8b-8c56-5ac83aff625a%2Fsg5h54i_processed.png&w=3840&q=75)
Transcribed Image Text:• Example 3. For the matrix M of the coefficients in equations (6.7) or (6.9), find M-1.
1
0 -1
M = -2
3
1
-3
2
We find det M = 3. The cofactors of the elements are:
3 0
= 6,
-3 2
-2 0
= 4,
-2
1st row :
3
= 3.
1
2
1
-3
1
1
1
2nd
= 3,
= 3,
= 3.
-3
row :
-3
2
2
|0
1 0
= 3.
-2 3
-1
1
-
3rd row :
- 3,
2,
-2
Then
6 4 3
C =
1
CT
det M
6 3 3
1
4 3 2
3
3 3 3
3 3 3
so M-1 -
= -
3 2 3
Now we can use M-1 to solve equations (6.9). By (6.12), the solution is given by
the column matrix r = M-'k, so we have
6 3 3
1
4 3 2
3
3 3 3,
-10
or x = 1, y = 1, z = -4. (See Problem 12.)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)