Question 1. The following system of linear equations has 2 parameters a, b e R: X1 = 1 X1 +x2 X1 +x2 +X3 = 3 = 6 +x2 +x3 + ax4 = b+6 1) Write the augmented matrix of the system and use elementary row operations to change it to a simpler form. 2) For what values of the parameters a, b does the system have a unique solution? Find that solution. 3) For what values of the parameters a, b does the system have no solution? 4) For what values of the parameters a, b does the system have infinitely many solutions? Find those solutions.
Question 1. The following system of linear equations has 2 parameters a, b e R: X1 = 1 X1 +x2 X1 +x2 +X3 = 3 = 6 +x2 +x3 + ax4 = b+6 1) Write the augmented matrix of the system and use elementary row operations to change it to a simpler form. 2) For what values of the parameters a, b does the system have a unique solution? Find that solution. 3) For what values of the parameters a, b does the system have no solution? 4) For what values of the parameters a, b does the system have infinitely many solutions? Find those solutions.
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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Transcribed Image Text:Question 1. The following system of linear equations has 2 parameters a, b E R:
X1
1
3
Xi +x2
X1 +x2 +x3
X1 +x2 +x3+ax4
= b+6
1) Write the augmented matrix of the system and use elementary row operations to change
it to a simpler form.
2) For what values of the parameters a, b does the system have a unique solution? Find
that solution.
3) For what values of the parameters a, b does the system have no solution?
4) For what values of the parameters a, b does the system have infinitely many solutions?
Find those solutions.
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