If $f(x)=\begin{vmatrix}0 & x-a& x-b\\x+a& 0 & x-c\\x+b & x+c& 0\end{vmatrix}$, then f(0) is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0
$f(x)=\begin{vmatrix}0 & x-a& x-b\\x+a& 0 & x-c\\x+b & x+c& 0\end{vmatrix}⇒f(0)=\begin{vmatrix}0 & -a& -b\\a& 0 & -c\\b & c& 0\end{vmatrix}$
as it is skew symmetric
$A=-A^T$
so $|A|=-|A^T|$
so $|A|=0$
so $f(0)=0$