Question

If $\left|\begin{array}{ccc}a& -b& -c\\ -a& b& -c\\ -a& -b& -c\end{array}\right|+\lambda abc=0$, then $\lambda$ is equal to

• A. $2$
• B. $4$
• C. $-2$
• D. $-4$

Answer 1

The correct option is B $4$

$\left|\begin{array}{ccc}a& -b& -c\\ -a& b& -c\\ -a& -b& -c\end{array}\right|+\lambda abc=0$

Substitute $a=b=c=1$

$\left|\begin{array}{ccc}1& -1& -1\\ -1& 1& -1\\ -1& -1& -1\end{array}\right|+\lambda =0$

$(-2-2)+\lambda =0$

$\Rightarrow \lambda =4$