Solveeit Logo
Login

Question

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| = λ a2b2c2, Then λ =

A

1

B

2

C

3

D

4

Answer

4

Explanation

Solution

Put a = 1; b = 1; c = 2

⇒ ∣–1121–1222–4∣\left| \begin{matrix} –1 & 1 & 2 \\ 1 & –1 & 2 \\ 2 & 2 & –4 \end{matrix} \right| = λ.4 ⇒ 16 = 4λ ⇒ λ = 4