Consider 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.
Consider 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.
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:Consider 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.
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