Let x,y,zbe a non-zero solution of the equation  x+λy+2z=0, 2x+λz=0 and  2λx−2y+3z=0 where λ∈R then the value of x+y−zy= ______

1λ220λ2λ-23=0⇒1(0+2λ)-λ6-2λ2+2(-4)=0⇒2λ-6λ+2λ3-8=0⇒2λ2-4λ-8=0⇒λ3-2λ-4=0 ⇒λ-2λ2+2λ+2=0 ⇒λ=2∴The given equations become          x+2y+2z=0, 2x+2z=0, 4x-2y+3z=0Solving, we getx+2y+2z=02x+2z=02y−x=0⇒x=2y Also, 4x-2y+3z=0⇒z=-2y∴x+y−zy=2y+y+2yy=5yy=5