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.