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Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question
![- Without using pencil and paper, determine which of the following homogeneous systems have nontrivial solutions.
(a) 2x1 – 3x2+ 4x3 – x4=0
7x1+ x2-&r3 + 9x4=0
2x1 + 8x2+ x3- x4=0
(b) x1 + 3x2- 13= 0
x2- 8r3 =0
4x3=0
(c) a}x1+a]2#2+ a13*3=0
(d) 3x1– 2x2=0
6x1 - 4x2 =0](https://content.bartleby.com/qna-images/question/6e0c1fdc-710a-4935-a514-b0e2eeac1aa2/962d367f-bf4b-4143-90d0-7ae75d603fac/oyr51d_thumbnail.png)
Transcribed Image Text:- Without using pencil and paper, determine which of the following homogeneous systems have nontrivial solutions.
(a) 2x1 – 3x2+ 4x3 – x4=0
7x1+ x2-&r3 + 9x4=0
2x1 + 8x2+ x3- x4=0
(b) x1 + 3x2- 13= 0
x2- 8r3 =0
4x3=0
(c) a}x1+a]2#2+ a13*3=0
(d) 3x1– 2x2=0
6x1 - 4x2 =0
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- Find all basic solutions to the following homogeneous system and express the general solution as a linear combination of these basic solutions: -2x1 + 2x2 ― x34x4x5 = 0 2x12x2 + 2x3 - 2x4 = 0 2x12x2 3x3 + x5 3x3x5 = = 0arrow_forwardFor what value of a does the system have nontrivial solutions: x1 + 2x2 + x3 = 0 - x1 - x2 + x3 = 0 3x1 + 4x2 + a* x3 = 0 O 1 -1arrow_forwardConsider the following system of linear equations: x + y 2x + 3y - Z = 6, - Z = 4, 2x+y+az = b. Use Gaussian elimination to find conditions on the constants a,b for which the above system of linear equations is: (i) inconsistent; (ii) consistent, with a unique solution; (iii) consistent, with an infinite number of solutions.arrow_forward
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