Question

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

• A. $4abc$
• B. $(a-b)(b-c)(c-a)$
• C. $(a+b+c{)}^3$
• D. 0

Answer 1

The correct option is D 0

$R_1\to \frac{R_1}{bc},R_2\to \frac{R_2}{ac},R_3\to \frac{R_3}{ab}$
$\left|\begin{array}{ccc}bc& 1& \frac{1}{b}+\frac{1}{c}\\ ca& 1& \frac{1}{c}+\frac{1}{a}\\ ab& 1& \frac{1}{a}+\frac{1}{b}\end{array}\right|$
$C\to \frac{C_1}{abc}then,C_3\to C_3+C_1$
$\left|\begin{array}{ccc}\frac{1}{a}& 1& \frac{1}{a}+\frac{1}{b}+\frac{1}{c}\\ \frac{1}{b}& 1& \frac{1}{a}+\frac{1}{b}+\frac{1}{c}\\ \frac{1}{c}& 1& \frac{1}{a}+\frac{1}{b}+\frac{1}{c}\end{array}\right|=0$
(Two columns identical)