A linear system is described by the following equations X1 - X2 + X3 = 1 4x1 + 3X2 - X3 %3D 3x1 + 5x2 + 3x3 4 Answer the following questions (1-4): Questions-1: Does this system has any unique solution? Explain. Question-2: Solve the above linear system by Gaussian elimination method. Now solve the same linear system above by the LU -decomposition method: Question-3: Find the lower triangular matrix L and the upper triangular matrix U. Question-4: Now find the solution of the

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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A linear system is described by the following
equations
X1 - X2 + X3
= 1
4x1 + 3X2 - X3
%3D
3x1 + 5x2 + 3x3
4
Answer the following questions (1-4):
Questions-1:
Does this system has any
unique solution? Explain.
Question-2:
Solve the above linear
system by Gaussian elimination method.
Now solve the same linear system above by the LU
-decomposition method:
Question-3:
Find the lower triangular
matrix L and the upper triangular matrix U.
Question-4:
Now find the solution of the
linear system again using the matrix L and U found
in the previous question.
Transcribed Image Text:A linear system is described by the following equations X1 - X2 + X3 = 1 4x1 + 3X2 - X3 %3D 3x1 + 5x2 + 3x3 4 Answer the following questions (1-4): Questions-1: Does this system has any unique solution? Explain. Question-2: Solve the above linear system by Gaussian elimination method. Now solve the same linear system above by the LU -decomposition method: Question-3: Find the lower triangular matrix L and the upper triangular matrix U. Question-4: Now find the solution of the linear system again using the matrix L and U found in the previous question.
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