Let Δ=|Ax x 2 1 By y 2 1 Cz z 2 1| and Δ1=|A B C x y z zy zx xy | then |A x B y C y x2 y2 z2 1 1 1|

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Tardigrade Admin · Accepted Answer

We have, Δ=[A x x2 1 B y y2 1 C z z2 1 ] and Δ1=[A B C x y z z y z x x y] Now, Δ1=[A B C X y Z z y z x x y ] On applying C1 arrow x C1, C2 arrow y C2, C3 arrow z C3, we get =(1/x y z)[A x B y C z x2 y2 z2 x y z x y z x y z ] Taking common xyz from R3 =(x y z/x y z)[A x B y C z x2 y2 z2 1 1 1] =[A x B y C z x2 y2 z2 1 1 1] =[A x x2 1 B y y2 1 C z z2 1] |∵| A'| A |] =Δ

Q. Let $Δ = ∣ ∣ A x B y C z x^{2} y^{2} z^{2} 111 ∣ ∣$ and $Δ_{1} = ∣ ∣ A x zy B y z x C z x y ∣ ∣$ then $∣ ∣ A x x^{2} 1 B y y^{2} 1 C y z^{2} 1 ∣ ∣$

$Δ_{1} = - Δ$

$Δ_{1} = Δ$

$Δ_{1} \neq = Δ$

$Δ_{1} = 2 Δ$

Q. Let Δ=∣∣​AxByCz​x2y2z2​111​∣∣​ and Δ1​=∣∣​Axzy​Byzx​Czxy​∣∣​ then ∣∣​Axx21​Byy21​Cyz21​∣∣​

Δ1​=−Δ

Δ1​=Δ

Δ1​=Δ

Δ1​=2Δ

Q. Let $Δ = ∣ ∣ A x B y C z x^{2} y^{2} z^{2} 111 ∣ ∣$ and $Δ_{1} = ∣ ∣ A x zy B y z x C z x y ∣ ∣$ then $∣ ∣ A x x^{2} 1 B y y^{2} 1 C y z^{2} 1 ∣ ∣$

$Δ_{1} = - Δ$

$Δ_{1} = Δ$

$Δ_{1} \neq = Δ$

$Δ_{1} = 2 Δ$