Question

∆­₁ = $\left| \begin{matrix} x & b & b \\ a & x & b \\ a & a & x \end{matrix} \right|$&∆₂ = $\left| \begin{matrix} x & b \\ a & x \end{matrix} \right|$, then –

• A. ∆₁ = 3 (∆₂)²
• B. $\frac{d}{dx}$ (∆₁) = 3∆₂
• C. $\frac{d}{dx}$ (∆₁) = 3 (∆₂)²
• D. ∆₁­ = 3(∆₂)^3/2

Answer 1

Answer: (B)

$\frac{d}{dx}$ (∆₁) = 3∆₂

Answer 2

Q $\frac{d}{dx}$ (∆₁) = $\left| \begin{matrix} 1 & 0 & 0 \\ a & x & b \\ a & a & x \end{matrix} \right|$ + $\left| \begin{matrix} x & b & b \\ 0 & 1 & 0 \\ a & a & x \end{matrix} \right|$+ $\left| \begin{matrix} x & b & b \\ a & x & b \\ 0 & 0 & 1 \end{matrix} \right|$

= 3 $\left| \begin{matrix} x & b \\ a & x \end{matrix} \right|$ = 3∆₂