If Δ1=|x a b b x a a b x| and Δ2=|x b a x| are the given determinants, then

Question

If Δ1=|x a b b x a a b x| and Δ2=|x b a x| are the given determinants, then (A) Δ1=3(Δ2)2 (B) (d/d x)(Δ1)=3 Δ2 (C) ( d / dx )(Δ1)=3(Δ2)2 (D) Δ1=3(Δ2)3 / 2

Tardigrade Admin · Accepted Answer

( d / dx )(Δ1)=|1 0 0 b x a a b x |+| x a b 0 1 0 a b x |+|x a b b x a 0 0 1| =| x a b x |+| x b a x |+| x a b x |=3 Δ2

Q. If $Δ_{1} = ∣ ∣ x b a a x b b a x ∣ ∣$ and $Δ_{2} = ∣ ∣ x a b x ∣ ∣$ are the given determinants, then

$Δ_{1} = 3 (Δ_{2})^{2}$

$\frac{d}{d x} (Δ_{1}) = 3 Δ_{2}$

$\frac{d}{d x} (Δ_{1}) = 3 (Δ_{2})^{2}$

$Δ_{1} = 3 (Δ_{2})^{3/2}$

$\frac{d}{d x} (Δ_{1}) = ∣ ∣ 1 b a 0 x b 0 a x ∣ ∣ + ∣ ∣ x 0 a a 1 b b 0 x ∣ ∣ + ∣ ∣ x b 0 a x 0 b a 1 ∣ ∣$
$= ∣ ∣ x b a x ∣ ∣ + ∣ ∣ x a b x ∣ ∣ + ∣ ∣ x b a x ∣ ∣ = 3 Δ_{2}$

Q. If Δ1​=∣∣​xba​axb​bax​∣∣​ and Δ2​=∣∣​xa​bx​∣∣​ are the given determinants, then

Δ1​=3(Δ2​)2

dxd​(Δ1​)=3Δ2​

dxd​(Δ1​)=3(Δ2​)2

Δ1​=3(Δ2​)3/2