Browse Questions

# Using the property of determinants, evalute: $\begin{vmatrix}x& x+y & x+2y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}$

$\begin{array}{1 1} 9y^2(x+y) \\ 9x^2(x+y) \\ y^2(x+y) \\ x^2(x+y) \end{array}$

$\Delta=\begin{vmatrix}x& x+y & x+2y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}$
Step 1: Apply $R_1\rightarrow R_1+R_2+R_3$
$\Delta=\begin{vmatrix}3x+3y& 3x+3y & 3x+3y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}$