The value of $\begin{vmatrix}1&a&a^2\\1&b&b^2\\1&c&c^2\end{vmatrix}$, is
Answer & explanation
Correct answer: option 1
We have,
$Δ=\begin{vmatrix}1&a&a^2\\1&b&b^2\\1&c&c^2\end{vmatrix}$
$⇒Δ=\begin{vmatrix}1&a&a^2\\0&b-a&b^2-a^2\\0&c-a&c^2-a^2\end{vmatrix}$ Applying $R_2 → R_2 - R_1$ and $R_3→R_3-R_1$
$⇒Δ=(b-a) (c-a)\begin{vmatrix}1&a&a^2\\0&1&b+a\\0&1&c+a\end{vmatrix}$ Taking $(b-a)$ and $(c-a)$ common from $R_2$ and $R_3$ respectively
$⇒Δ=(b-a) (c-a) (c-b)=(a-b) (b-c) (c-a)$