List of top Engineering Mathematics Questions on Matrices asked in GATE AE

The following system of linear equations \[ 7x-3y+z=0,\quad 3x-y+z=0,\quad x-y-z=0 \] has:

The system of equations \[ \begin{cases} x-2y+\alpha z=0,
2x+y-4z=0,
x-y+z=0 \end{cases} \] has a non-trivial solution for \(\alpha=\;\underline{\hspace{1cm}}\). \;(Answer in integer)