The following system of equations
has a unique solution. The only possible value(s) for α is/are
(A) 0
(B) either 0 or 1
(C) one of 0, 1 or -1
(D) any real number
(E) any real number other than 5
Answer: (E)
Explanation: The choice E was not there in GATE paper. We have added it as the given 4 choices don’t seem correct.
Augment the given matrix as 1 1 2 | 1 1 2 3 | 2 1 4 a | 4 Apply R2 <- R2 - R1 and R3 <- R3 - R1 1 1 2 | 1 0 1 1 | 1 0 3 a-2 | 3 Apply R3 <- R3 - 3R2 1 1 2 | 1 0 1 1 | 1 0 0 a-5 | 0 So for the system of equations to have a unique solution, a - 5 != 0 or a != 5 or a = R - {5}
Thanks to Anubhav Gupta for providing above explanation.
Readers can refer below MIT video lecture for linear algebra.
https://www.youtube.com/watch?v=QVKj3LADCnA&index=2&list=PLE7DDD91010BC51F8
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