Question

If ${\Delta }_1=\left|\begin{array}{ccc}1& 1& 1\\ a& b& c\\ a^2& b^2& c^2\end{array}\right|,{\Delta }_2=\left|\begin{array}{ccc}1& a& bc\\ 1& b& ca\\ 1& c& ab\end{array}\right|$ then

• A. ${\Delta }_1+{\Delta }_2=0$
• B. ${\Delta }_1={\Delta }_2$
• C. ${\Delta }_1+2{\Delta }_2=0$
• D. ${\Delta }_1-2{\Delta }_2=0$

Answer 1

Answer: (B)

${\Delta }_2=\left|\begin{array}{ccc}1& a& bc\\ 1& b& ca\\ 1& c& ab\end{array}\right|\frac{abc}{abc}$
$=\frac{1}{abc}\left|\begin{array}{ccc}a& a^2& abc\\ b& b^2& abc\\ c& c^2& abc\end{array}\right|=\left|\begin{array}{ccc}1& a& a^2\\ 1& b& b^2\\ 1& c& c^2\end{array}\right|={\Delta }_1$