Question

The value of the determinant $\begin{vmatrix}b c & a c & a b \\ a & b & c \\ a^{3} & b^{3} & c^{3}\end{vmatrix}$ is

• A. $(a+ b+ c)$
• B. $a+b+c-a b$
• 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)

$C_{1} \rightarrow a C_{1}, C_{2} \rightarrow b C_{2}, C_{3} \rightarrow c C_{3}$
Then, $\Delta=\begin{vmatrix}1 & 1 & 1 \\ a^{2} & b^{2} & c^{2} \\ a^{4} & b^{4} & c^{4}\end{vmatrix}=\left(a^{2}-b^{2}\right)\left(b^{2}-c^{2}\right)\left(c^{2}-a^{2}\right)$