If the system of equations 2x+3y−z=0, x+ky−2z=0and 2x−y+z=0has a non – trivial solution x,y,zthen xy+yz+zx+k=

Since the system has non-trivial solution, we have Δ=0⇒23−11k−22−11=0 ⇒2k-2-31+4-1-1-2k=0 ⇒k= 9/2,then equations are 2x+3y−z=0,2x−y+z=0⇒4y=2z⇒2y=z,x=-y/2∴xy+yz+zx+k=-12+12-4+92=12