Q219 / 270 · NDA 2011 (Phase 2) · Mathematics

If $a^{-1}+b^{-1}+c^{-1}=0$ such that $\left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|=\lambda$, then what is $\lambda$ equal to?

  • A
    $-a b c$
  • B
    $a b c$
  • Correct answer
    C
    $0$
  • D
    $1$

Solution

We have, $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0$ $\begin{aligned} & \therefore\left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|=a b c\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=0 \\ & \Rightarrow \lambda=0 .\end{aligned}$

Hence, the correct answer is option: 'C'.

Relevant Questions