Question

If D₁ = $\left| \begin{matrix} f & 2d & e \\ 2z & 4x & 2y \\ e & 2a & b \end{matrix} \right|$ and D₂= $\left| \begin{matrix} 2a & b & e \\ 2d & e & f \\ 4x & 2y & 2z \end{matrix} \right|$ Then $\frac{\Delta_{1}}{\Delta_{2}}$ =

• A. 1
• B. 2
• C. $\frac{1}{2}$
• D. None of these

Answer 1

Answer: (A)

1

Answer 2

D₁ = – $\left| \begin{matrix} 2d & f & e \\ 4x & 2z & 2y \\ 2a & e & b \end{matrix} \right|$ (c₁ ↔ c₂)

= +$\left| \begin{matrix} 2d & e & f \\ 4x & 2y & 2z \\ 2a & b & e \end{matrix} \right|$ (c₂ ↔ C₃) = – $\left| \begin{matrix} 2a & b & e \\ 4x & 2y & 2z \\ 2d & e & f \end{matrix} \right|$

=$\left| \begin{matrix} 2a & b & e \\ 2d & e & f \\ 4x & 2y & 2z \end{matrix} \right|$ = D₂ \$\frac{\Delta_{1}}{\Delta_{2}}$ = 1