Δ1=|y5 z6(z3-y3) x4 z6(x3-z3) x4 y5(y3-x3) y2 z3(y6-z6) x z3(z6-x6) x y2(x6-y6) y2 z3(z3-y3) x z3(x3-z3) x y2(y3-x3)| and Δ2=|x y2 z3 x4 y5 z6 x7 y8 z9| Then Δ1 Δ2 is equal to

Question

Δ1=|y5 z6(z3-y3) x4 z6(x3-z3) x4 y5(y3-x3) y2 z3(y6-z6) x z3(z6-x6) x y2(x6-y6) y2 z3(z3-y3) x z3(x3-z3) x y2(y3-x3)| and Δ2=|x y2 z3 x4 y5 z6 x7 y8 z9| Then Δ1 Δ2 is equal to (A) Δ23 (B) Δ22 (C) Δ24 (D) None of these

Tardigrade Admin · Accepted Answer

The given determinant Δ1 is obtained by corresponding cofactors of determinant Δ2; hence Δ1=Δ22. Now Δ L Δ2=Δ22 Δ2=Δ23

$Δ_{2}^{3}$

$Δ_{2}^{2}$

$Δ_{2}^{4}$

None of these

The given determinant $Δ_{1}$ is obtained by corresponding cofactors of determinant $Δ_{2}$ ; hence $Δ_{1} = Δ_{2}^{2}$ .
Now $Δ_{L} Δ_{2} = Δ_{2}^{2} Δ_{2} = Δ_{2}^{3}$

Q. Δ1​=∣∣​y5z6(z3−y3)y2z3(y6−z6)y2z3(z3−y3)​x4z6(x3−z3)xz3(z6−x6)xz3(x3−z3)​x4y5(y3−x3)xy2(x6−y6)xy2(y3−x3)​∣∣​ and Δ2​=∣∣​xx4x7​y2y5y8​z3z6z9​∣∣​ Then Δ1​Δ2​ is equal to

Δ23​

Δ22​

Δ24​

None of these

The given determinant Δ1​ is obtained by corresponding cofactors of determinant Δ2​; hence Δ1​=Δ22​. Now ΔL​Δ2​=Δ22​Δ2​=Δ23​

$Δ_{2}^{3}$

$Δ_{2}^{2}$

$Δ_{2}^{4}$

The given determinant $Δ_{1}$ is obtained by corresponding cofactors of determinant $Δ_{2}$ ; hence $Δ_{1} = Δ_{2}^{2}$ .
Now $Δ_{L} Δ_{2} = Δ_{2}^{2} Δ_{2} = Δ_{2}^{3}$