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

The condition for a homogeneous system of equations to have a non-trivial solution is Δ=0⇒1k-33k-223-4=0⇒1−4k+6−k−12+4−39−2k=0⇒−4k+6+8k−27+6k=0⇒10k−21=0⇒k=2110