If \( A=\begin{bmatrix}x & p & x+p\\y & q & y+q\\z & r & z+r\end{bmatrix} \), then \( |A| \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0
The third column is the sum of the first two columns, so the operation \( C_3\to C_3-C_1-C_2 \) turns it into zeros:
\( \displaystyle |A|=\begin{vmatrix}x & p & x+p-x-p\\y & q & y+q-y-q\\z & r & z+r-z-r\end{vmatrix} \)
\( \displaystyle =\begin{vmatrix}x & p & 0\\y & q & 0\\z & r & 0\end{vmatrix} \)
\( \displaystyle =0 \)
A determinant with a column of zeros is 0.