AP EAMCET · Maths · Determinants
For any \(a, b, c \in \mathbf{R}\), the determinant \(\left|\begin{array}{lll}b c & b+c & 1 \\ c a & c+a & 1 \\ a b & a+b & 1\end{array}\right|\) is equal to
- A \(a\left(b^2-c^2\right)+b\left(c^2-a^2\right)+c\left(a^2-b^2\right)\)
- B \(a(b-c)+b(c-a)+c(a-b)\)
- C \((a-b)(b-c)(c-a)\)
- D \(a b c\)
Answer & Solution
Correct Answer
(C) \((a-b)(b-c)(c-a)\)
Step-by-step Solution
Detailed explanation
For any \(a, b, c \in \mathbf{R}\), the given determinant \(\Delta=\left|\begin{array}{lll} b c & b+c & 1 \\ c a & c+a & 1 \\ a b & a+b & 1 \end{array}\right|\) On applying \(R_2 \rightarrow R_2-R_1\) and \(R_3 \rightarrow R_3-R_1\), we have…
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