In the following linear system, x+2y+ 7z = 5 x+3y+ 9z = 7 x+2y+ (a2+3)z = a+7 determine all values of a for which the resulting linear system has (a) no solution (b) a unique solution (c) infinitely many solutions Justify your answer for each. Reduce the system via row operations, then analyze.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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In the following linear system,

x+2y+ 7z = 5

x+3y+ 9z = 7

x+2y+ (a2+3)z = a+7

determine all values of a for which the resulting linear system has

(a) no solution

(b) a unique solution

(c) infinitely many solutions

Justify your answer for each. Reduce the system via row operations, then analyze.     

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