Evaluate the determinant ofthe 3by3 matrix [ x y z ,a − x b − y c − z, a b c]

Question

Evaluate the determinant:

 \(\begin{vmatrix}x&y&z\\a-x&b-y&c-z\\a&b&c\end{vmatrix}\)  

Answer 1

\(\begin{vmatrix}x&y&z\\a-x&b-y&c-z\\a&b&c\end{vmatrix}\) = \(\begin{vmatrix}x&y&z\\a&b&c\\a&b&c\end{vmatrix}\) (On applying R₂ + R₂ + R₁)

 = 0 (Row R₂ is similar to row R₃)