Consider the matrix A = [[5, -4], [k, -1]] where k is a constant. If the determinant of A is 3, then the ratio of the largest eigenvalue of A to the constant k...

Which of the following statement(s) is/are true with respect to eigenvalues and eigenvectors of a matrix?

The system of equations x - 2y + αz = 0, 2x + y - 4z = 0, x - y + z = 0 has a non-trivial solution for α = ______. (Answer in integer)