Which of the following is a factor of the determinant $\begin{vmatrix} a & b & c\\b & c & a\\c & a & b\end{vmatrix}$ ?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $a+b+c$
$Δ=\begin{vmatrix} a & b & c\\b & c & a\\c & a & b\end{vmatrix}$
$C_1→C_1+C_2+C_3$
$\begin{vmatrix} a+b+c & b & c\\a+b+c & c & a\\a+b+c & a & b\end{vmatrix}$
$=(a+b+c)\begin{vmatrix} 1 & b & c\\1 & c & a\\1 & a & b\end{vmatrix}$
$⇒(a+b+c)$ is a better