Question

If A = is skew symmetric matrix $$\left[\begin{array}{ccc}a& 2& -3\\ b& c& 5\\ d& e& f\end{array}\right]$$
Then a + b + c + d + e + f =

• A. 3
• B. -3
• C. 4
• D. -4

Answer 1

The correct option is D -4

Given $A=\left[\begin{array}{ccc}a& 2& -3\\ b& c& 5\\ d& e& f\end{array}\right]$ is skew - symmetric
$\Rightarrow A=-A^T\Rightarrow \left[\begin{array}{ccc}a& 2& -3\\ b& c& 5\\ d& e& f\end{array}\right]=-\left[\begin{array}{ccc}a& b& d\\ 2& c& e\\ -3& 5& f\end{array}\right]$
$\Rightarrow a=-a\Rightarrow 2a=0\Rightarrow a=0$
b = -2
d = 3
$c=-c\Rightarrow 2c=0\Rightarrow c=0$
e = -5
$f=-f\Rightarrow 2f=0\Rightarrow f=0$
$\Rightarrow a+b+c+d+e+f=-4$