Practicing Success
If x - y = 2 and y - z = 3 then value of, \(\begin{vmatrix}1 & x & x^2\\1 & y & y^2\\1 & z & z^2\end{vmatrix}=\) |
6 -10 -15 -30 |
-30 |
x - y = 2 and y - z = 3 , z-x = -5 \(\begin{vmatrix}1 & x & x^2\\1 & y & y^2\\1 & z & z^2\end{vmatrix}\) $R_2 → R_2 - R_1$ $R_3 → R_3 - R_1$ \(=\begin{vmatrix}1 & x & x^2\\0 & y-x & (y-x)(y+x)\\0 & z-x & (z-x)(z+x)\end{vmatrix}\) \((y-x)(z-x)\begin{vmatrix}1 & x & x^2\\0 & 1 & y+x\\0 & 1 & z+x\end{vmatrix}\) $=(y-x)(z-x)[1.(1.(z+x)-1.(y+x)]$ $=(y-x)(z-x)[z+x-y-x]$ $=(x-y)(y-z)(z-x)$ $=(2)(3)(z-x)=6\times -5 = -30$ |