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AP EAMCET · Maths · Determinants

If \(a, b, c\) are distinct positive real numbers, then the value of the determinant \(\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|\) is

  1. A \( < 0\)
  2. B \(>0\)
  3. C \(0\)
  4. D \(\geq 0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \( < 0\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { Let } \mathrm{A}=\left|\begin{array}{lll} a & b & c \\ b & c & a \\ c & a & b \end{array}\right| \quad\left[\mathrm{C}_1 \rightarrow \mathrm{C}_1 \rightarrow \mathrm{C}_2 \rightarrow \mathrm{C}_3\right] \\ & =\left|\begin{array}{lll} a+b+c & b & c \\…