Question

The value of $\left|\begin{array}{ccc}\frac{1}{a}& a^2& bc\\ \frac{1}{b}& b^2& ca\\ \frac{1}{c}& c^2& ab\end{array}\right|$ is equal to

• A. $abc$
• B. $a+b+c$
• C. $0$
• D. $4abc$

Answer 1

Answer: (C)

$0$

Let $\Delta =\left|\begin{array}{ccc}\frac{1}{a}& a^2& bc\\ \frac{1}{b}& b^2& ca\\ \frac{1}{c}& c^2& ab\end{array}\right|$

Take $abc$ common from third column we get,

$\Delta =abc\left|\begin{array}{ccc}\frac{1}{a}& a^2& \frac{1}{a}\\ \frac{1}{b}& b^2& \frac{1}{b}\\ \frac{1}{c}& c^2& \frac{1}{c}\end{array}\right|=abc\left(0\right)=0$

Since first and third column are same.