engineering recuitment GATE IN Test Series 2023-24 Mock Test Engineering Mathematics Linear Algebra Eigenvalues
We have a set of 3 linear equations in 3 unknowns. ‘X ≡ Y’ means X and Y are equivalent statements and ‘X ≢ Y’ means X and Y are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero.
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?1
P ≡ R ≡ Q ≡ S
2
P ≡ R ≢ Q ≡ S
3
P ≡ Q ≢ R ≡ S
4
P ≢ Q ≢ R ≢ S