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Determine the values of a such that the following system of linear equations have i) no solution ii) more than one solution and iii) unique solution: x + y + 7z = -7 2x + 3y + 17z = -16 x + 2y + (a² + 1)z = 3a %3| %3D

Determine the values of a such that the following system of linear equations have i) no solution ii) more than one solution and iii) unique solution: x + y + 7z = -7 2x + 3y + 17z = -16 x + 2y + (a² + 1)z = 3a %3| %3D

Advanced Engineering Mathematics
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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Determine the values of a such that the following system of linear equations have i) no solution ii) more than one solution and iii) unique solution: x + y + 7z = -7 2x + 3y + 17z = -16 x + 2y + (a² + 1)z = 3a (b) Given that v = (2, –5, 3), vị = (1, –3, 2), v2 = (2, –4, – 1), v3 = (1,–5, 7) Express v as a linear combination of vị, v2, v3. (c) Using Gaussian elimination method Examine the consistency of the following system of linear equations: I| 2х1 + 2x2 + 2xз — Зх4 3D 2 2x1 + x2 + 5x3 + x4 = 5 Зx1 + 6х2 — 2хз + x4 —D 8 2.
Transcribed Image Text:Determine the values of a such that the following system of linear equations have i) no solution ii) more than one solution and iii) unique solution: x + y + 7z = -7 2x + 3y + 17z = -16 x + 2y + (a² + 1)z = 3a (b) Given that v = (2, –5, 3), vị = (1, –3, 2), v2 = (2, –4, – 1), v3 = (1,–5, 7) Express v as a linear combination of vị, v2, v3. (c) Using Gaussian elimination method Examine the consistency of the following system of linear equations: I| 2х1 + 2x2 + 2xз — Зх4 3D 2 2x1 + x2 + 5x3 + x4 = 5 Зx1 + 6х2 — 2хз + x4 —D 8 2.
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