Question
The system of linear equations x+λy−z=0; λx−y−z=0; x+y−λz=0 has a non-trivial solution for
-
infinitely many values of λ.
-
exactly one value of λ.
-
exactly two values of λ.
-
exactly three values of λ.
Solution
D.
exactly three values of λ.
Given system of linear equations is
x+λy−z=0;
λx−y−z=0;
x+y−λz=0
Note that, given system will have a non-trivial solution only if the determinant of the coefficient matrix is zero, ie.
Hence, given system of linear equation has a non-trivial solution for exactly three values of λ.
