In excenopse 12, solve the given system the method of example 3.35 using 12. 24₁- 42 = 1 241 +12 =२
In excenopse 12, solve the given system the method of example 3.35 using 12. 24₁- 42 = 1 241 +12 =२
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
100%
I have added example 3.25 as per the question
![Example 3.25
Use the inverse of the coefficient matrix to solve the linear system
x + 2y =
3
3x + 4y =
-2
Solution The coefficient matrix is the matrix A =
whose inverse we com-
puted in Example 3.24. By Theorem 3.7, Ax = b has the unique solution x = A¯¹b.
Here we have b = ; thus, the solution to the given system is
3
[-]
-DAN-D
X =
2
-8
Remark Solving a linear system Ax = b via x = A¹b would appear to be a good
method. Unfortunately, except for 2 X 2 coefficient matrices and matrices with cer-
tain special forms, it is almost always faster to use Gaussian or Gauss-Jordan elimi-
nation to find the solution directly. (See Exercise 13.) Furthermore, the technique of
Example 3.25 works only when the coefficient matrix is square and invertible, while
elimination methods can always be applied.
Properties of Invertible Matrices
The following theorem records some of the most important properties of invertible
matrices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46695490-535e-4e6d-be60-a5ac8c464218%2Fe83a4f7d-d132-4a71-8cf1-a9943c2e4ac3%2F85zs56s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Example 3.25
Use the inverse of the coefficient matrix to solve the linear system
x + 2y =
3
3x + 4y =
-2
Solution The coefficient matrix is the matrix A =
whose inverse we com-
puted in Example 3.24. By Theorem 3.7, Ax = b has the unique solution x = A¯¹b.
Here we have b = ; thus, the solution to the given system is
3
[-]
-DAN-D
X =
2
-8
Remark Solving a linear system Ax = b via x = A¹b would appear to be a good
method. Unfortunately, except for 2 X 2 coefficient matrices and matrices with cer-
tain special forms, it is almost always faster to use Gaussian or Gauss-Jordan elimi-
nation to find the solution directly. (See Exercise 13.) Furthermore, the technique of
Example 3.25 works only when the coefficient matrix is square and invertible, while
elimination methods can always be applied.
Properties of Invertible Matrices
The following theorem records some of the most important properties of invertible
matrices.
Transcribed Image Text:In excerepse 12, solve the given system
the method of en
example 3.35
using
12. 2₁ 4₂ = 1
241 +12 =२
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
