Xi+x2 =1 - ах, +x, + (a-1)x, — -1 -x3 =-1 (1- a)x, +(1-a)x, - 3x; - 2x4 =-1 where a is real number. a) Using rank information, detemine the condition(s) on a such that the given system has a unique solution b) Using only Gauss Elimination Method, determine the values for x1, X2, X3 and x4 for a=3. (Eaci step should be clearhy exmlained and its numerical outcome should be given.)

Xi+x2 =1 - ах, +x, + (a-1)x, — -1 -x3 =-1 (1- a)x, +(1-a)x, - 3x; - 2x4 =-1 where a is real number. a) Using rank information, detemine the condition(s) on a such that the given system has a unique solution b) Using only Gauss Elimination Method, determine the values for x1, X2, X3 and x4 for a=3. (Eaci step should be clearhy exmlained and its numerical outcome should be given.)

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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Question

Consider the following system of linear equations.

X1 +x2 =1
- ax, +x, + (a – 1)x, = -1
-X; =-1
(1- a)x, +(1-a)x, - 3x; - 2x4 = -1
where a is real number.
a) Using rank information, detemine the condition(s) on a such that the given system has a unique
solution
b) Using only Gauss Elimination Method, detemine the values for x1, x2, x3 and x4 for a=3. (Each
step should be clearly explained and its numerical outcome should be given.)

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