Using the property of determinants and without expanding, prove that: \(\begin{vmatrix}x&a&x+a\\y&b&y+b\\z&C&z+c\end{vmatrix}=0\)
\(\begin{vmatrix}x&a&x+a\\y&b&y+b\\z&C&z+c\end{vmatrix}\)
=\(\begin{vmatrix}x&a&x\\y&b&y\\z&c&z\end{vmatrix}+\begin{vmatrix}x&a&a\\y&b&b\\z&c&c\end{vmatrix}=0+0=0\)
[Here the two columns of the determinants are identical]
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Read More: Properties of Determinants