COMEDK · Maths · 22. Determinants
The value of \(\left|\begin{array}{lll}x & p & q \\ p & x & q \\ p & q & x\end{array}\right|\) is
- A \((x-p)(x-q)(x+p+q)\)
- B \(x(x-p)(x-q)\)
- C \(p q(x-p)(x-q)\)
- D \((p-q)(x-q)(x-p)\)
Answer & Solution
Correct Answer
(A) \((x-p)(x-q)(x+p+q)\)
Step-by-step Solution
Detailed explanation
We have \[ \left[\begin{array}{lll} x & p & q \\ p & x & q \\ p & q & x \end{array}\right] \] Applying \(C_{1} \rightarrow C_{1}+C_{2}+C_{33}\), we get \[ \left|\begin{array}{lll} x+p+q & p & q \\ x+p+q & x & q \\ x+p+q & q & x \end{array}\right| \] Taking common \((x+p+q)\)…
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