5. Let k be a real number. Consider the following linear system:x + y + z = kkx + y + 2z = 2x + ky + z = 4Find all possible values of k such that system (1)(i) has a unique solution;(ii) has no solutions;(iii) has infinitely many solutions.

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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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Find all possible values of k such that system (1) (i) has a unique solution; (ii) has no solutions; (iii) has infinitely many solutions.