Matrix Algebra - General Aptitude - General Aptitude (GA) Previous Year Questions

If the sum of the diagonal elements of a \( 2 \times 2 \) matrix is \( -6 \), then the maximum possible value of determinant of the matrix is __________.

The maximum value of \(\alpha\) such that the matrix \(\begin{pmatrix} -3 & 0 & -2 \\ 1 & -1 & 0 \\ 0 & \alpha & -2 \end{pmatrix}\) has three linearly independent real eigenvectors is

We have a set of 3 linear equations in 3 unknowns. ‘\(X \equiv Y\)’ means \(X\) and \(Y\) are equivalent statements and ‘\(X \not\equiv Y\)’ 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?