CUET · MATHS · PYQ PAPER 2023
The value of the determinant \(\left|\begin{array}{lll}a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1\end{array}\right|\) is:
- A Zero
- B a + b + c - 3abc
- C (a - b)(b - c)(a - c)
- D \(a^2+b^2+c^2-a b c\)
Answer & Solution
Correct Answer
(C) (a - b)(b - c)(a - c)
Step-by-step Solution
Detailed explanation
\(\left| \begin{array}{lll} a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1 \end{array} \right| = a^2(b \cdot 1 - 1 \cdot c) - a(b^2 \cdot 1 - 1 \cdot c^2) + 1(b^2 \cdot c - b \cdot c^2)\) \(= a^2(b-c) - a(b^2-c^2) + bc(b-c)\) \(= a^2(b-c) - a(b-c)(b+c) + bc(b-c)\)…
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