The value of the determinant \(\begin{vmatrix}a - b & b - c & c - a\\ x - y & y - z & z - x\\ p - q & q - r & r - p\end{vmatrix}\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0
In every row the three entries add up to zero, for example \((a - b) + (b - c) + (c - a) = 0\).
Applying \(C_1 \to C_1 + C_2 + C_3\), which does not change the value:
\( \displaystyle \Delta = \begin{vmatrix}0 & b - c & c - a\\ 0 & y - z & z - x\\ 0 & q - r & r - p\end{vmatrix} \)
A determinant with a column of zeros is zero, so \(\Delta = 0\) for all values of the letters.