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Question: If \(\left| \begin{matrix} –a^{2} & ab & ac \\ ab & –b^{2} & bc \\ ac & bc & –c^{2} \end{matrix} \ri...

If ∣–a2abacab–b2bcacbc–c2∣\left| \begin{matrix} –a^{2} & ab & ac \\ ab & –b^{2} & bc \\ ac & bc & –c^{2} \end{matrix} \right| = la2b2c2, then the value of l is –

A

1

B

2

C

4

D

3

Answer

4

Explanation

Solution

Put a = b = c = 1

∣ 6mu–1111−1111−1 6mu∣\left| \mspace{6mu}\begin{matrix} –1 & 1 & 1 \\ 1 & - 1 & 1 \\ 1 & 1 & - 1 \end{matrix}\mspace{6mu} \right| = l × 1 × 1 × 1

l = –1 (1 –1) – 1 (–1 –1) + 1 (1 + 1)

l = 0 + 2 + 2 Ž l = 4