Question

Evaluate$\begin{vmatrix} 1 & x & y\\\ 1 & x+y & y\\\1&x&x+y \end{vmatrix}$

Answer 1

Δ=$$\begin{vmatrix} 1 & x & y\\\ 1 & x+y & y\\\1&x&x+y \end{vmatrix}
Applying $R_2\rightarrow R_2-R_1$ and $R_3\rightarrow R_3-R_1$,we have
Δ=$$\begin{vmatrix} 1 & x & y\\\ 0 & y & 0\\\0&0&x \end{vmatrix}

Expanding along $C_1$,we have:
$Δ=1(xy-0)=xy$