If the system of linear equationsx+ky+3z=0,   3x+ky−2z=0,2x+4y−3z=0 has a non – zero solution x,y,zThen x zy2is equal to

A homogeneous system of equations has non-zero solution if Δ=0⇒1k33k-224-3=0 ⇒1-3k+8-k-9+4+312-2k=0 ⇒4k=44  ⇒K=11    ∴The given equations become               x+11y+3z=0→(1) 3x+11y−2z=0→(2)     2x+4y−3z=0→(3)(1)  +  (3) ⇒3x+15y=0   ⇒x=−5y     Put x=-5yin equation (1), Le  get,−5y+11y+3z=0  ⇒Z=−2y∴  xzy2=−5y×−2yy2=10