Question

If $a,b$ & $c$ are non-zero real numbers then $D=\left|\begin{array}{ccc}{b}^2{c}^2& bc& b+c\\ c^2{a}^2& ac& a+c\\ a^2{b}^2& ab& a+b\end{array}\right|=$

• A. $abc$
• B. $a^2{b}^2{c}^2$
• C. $bc+ca+ab$
• D. zero

Answer 1

The correct option is D zero

$D=\left|\begin{array}{ccc}{b}^2{c}^2& bc& b+c\\ c^2{a}^2& ac& a+c\\ a^2{b}^2& ab& a+b\end{array}\right|puta=b=c=1D=\left|\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right|\because Dhastworoworcolumnareidentical.\therefore D=0.$