The value of k  for which the system of equations x+ky+3z=0 ,  3x+ky−2z=0  and 2x+3y−4z=0  has a non trivial solution is

The given system of equations have a non-trivial solution only if1k33k−223−4=0i.e., if −4k+6−k(−12+4)+3(9−2k)=0i.e., if −4k+6+8k+27−6k=0i.e., if −2k=−33  i.e., if k=332 .