The number of real values of 'a', for which the system of equations $2x+3y+az = 0$, $x+ay-2z=0$ and $3x+y+3z = 0$ has nontrivial solutions is
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For homogeneous systems, always check $\det(A)=0$ for non-trivial solutions. If the resulting equation has no real roots, then no such real parameter exists.