GATE 2014 [Set-3]
December 11, 2023Question 12334 – APPSC-PL-2020-Technical-Paper
December 11, 2023GATE 2008
| Question 3 |
The following system of equations
-
x1 + x2 + 2x3 = 1
x1 + 2x2 + 3x3 = 2
x1 + 4x2 + ax3 = 4
has a unique solution. The only possible value(s) for a is/are
| 0 | |
| either 0 or 1 | |
| one of 0, 1 or -1 | |
| any real number |
Question 3 Explanation:
The conjugate matrix [A|B] is
When a-5 = 0, then rank(A) = rank[A|B]<3,
So infinite number of solutions.
But, it is given that the given system has unique solution
i.e., rank(A) = rank[A|B] = 3 will be retain only if a-5 ≠ 0.
When a-5 = 0, then rank(A) = rank[A|B]<3,
So infinite number of solutions.
But, it is given that the given system has unique solution
i.e., rank(A) = rank[A|B] = 3 will be retain only if a-5 ≠ 0.
Correct Answer: D
Question 3 Explanation:
The conjugate matrix [A|B] is
When a-5 = 0, then rank(A) = rank[A|B]<3,
So infinite number of solutions.
But, it is given that the given system has unique solution
i.e., rank(A) = rank[A|B] = 3 will be retain only if a-5 ≠ 0.
When a-5 = 0, then rank(A) = rank[A|B]<3,
So infinite number of solutions.
But, it is given that the given system has unique solution
i.e., rank(A) = rank[A|B] = 3 will be retain only if a-5 ≠ 0.