The value of the determinant
\(D=\begin{vmatrix} x & a & a+x\\y & b & b+y\\z & c & c+z\end{vmatrix}\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
Each element of the third column is the sum of the elements of the first two columns in its row: \(C_3 = C_1 + C_2\).
Applying \(C_3 \to C_3 - C_1 - C_2\), which does not change the value:
\( \displaystyle D = \begin{vmatrix} x & a & 0\\ y & b & 0\\ z & c & 0\end{vmatrix} \)
A determinant with a column of zeros is zero, so D = 0.