Question

The value of the determinant $\left|\begin{array}{ccc}bc& ac& ab\\ a& b& c\\ a^3& b^3& c^3\end{array}\right|$ is

• A. $(a+b+c)$
• B. $a+b+c-ab$
• C. $\left(a^2-b^2\right)\left(b^2-c^2\right)\left(c^2-a^2\right)$
• D. $a^2+b^2+c^2$

Answer 1

Answer: (C)

$C_1\to a{C}_1,C_2\to b{C}_2,C_3\to c{C}_3$
Then, $\Delta =\left|\begin{array}{ccc}1& 1& 1\\ a^2& b^2& c^2\\ a^4& b^4& c^4\end{array}\right|=\left(a^2-b^2\right)\left(b^2-c^2\right)\left(c^2-a^2\right)$