Question

If D₁ = $\left| \begin{matrix} x & b & b \\ a & x & b \\ a & a & x \end{matrix} \right|$ and D₂ = $\left| \begin{matrix} x & b \\ a & x \end{matrix} \right|$ are the given

determinants, then -

• A. D₁ = 3(D₂)²
• B. $\frac{d}{dx}$ (D₁) = 3D₂
• C. $\frac{d}{dx}$ (D₁) = 3D₂²
• D. D₁ = 3(D₂)^3/2

Answer 1

Answer: (B)

$\frac{d}{dx}$ (D₁) = 3D₂

Answer 2

$\frac{d}{dx}$ (D₁) =$\left| \begin{matrix} 1 & 0 & 0 \\ a & x & b \\ a & a & x \end{matrix} \right|$+$\left| \begin{matrix} x & b & b \\ 0 & 1 & 0 \\ a & a & x \end{matrix} \right|$+$\left| \begin{matrix} x & b & b \\ a & x & b \\ 0 & 0 & 1 \end{matrix} \right|$

= $\left| \begin{matrix} x & b \\ a & x \end{matrix} \right|$+$\left| \begin{matrix} x & b \\ a & x \end{matrix} \right|$+$\left| \begin{matrix} x & b \\ a & x \end{matrix} \right|$ = 3D₂