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Question: \[\left| \begin{matrix} a - b & b - c & c - a \\ x - y & y - z & z - x \\ p - q & q - r & r - p \end...

a - b & b - c & c - a \\ x - y & y - z & z - x \\ p - q & q - r & r - p \end{matrix} \right| =$$
A

a(x+y+z)+b(p+q+r)+ca(x + y + z) + b(p + q + r) + c

B

0

C

abc+xyz+pqrabc + xyz + pqr

D

None of these

Answer

0

Explanation

Solution

∣a−bb−cc−ax−yy−zz−xp−qq−rr−p∣=∣0b−cc−a0y−zz−x0q−rr−p∣\left| \begin{matrix} a - b & b - c & c - a \\ x - y & y - z & z - x \\ p - q & q - r & r - p \end{matrix} \right| = \left| \begin{matrix} 0 & b - c & c - a \\ 0 & y - z & z - x \\ 0 & q - r & r - p \end{matrix} \right| = 0

[by C1→C1+C2+C3]C_{1} \rightarrow C_{1} + C_{2} + C_{3}\rbrack