Practicing Success
The value of $\begin{vmatrix}1&a&a^2\\1&b&b^2\\1&c&c^2\end{vmatrix}$, is |
$(a-b) (b-c) (c-a)$ $(a^2-b^2) (b^2-c^2) (c^2-a^2)$ $(a-b+c) (b-c+a) (c-a+b)$ none of these |
$(a-b) (b-c) (c-a)$ |
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 $⇒Δ=(b-a) (c-a) (c-b)=(a-b) (b-c) (c-a)$ |