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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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.
In excerepse 12, solve the given system the method of en example 3.35 using 12. 2₁ 4₂ = 1 241 +12 =२
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
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