Question

If A=$\left|\begin{array}{ccc}a& b& c\\ x& y& z\\ l& m& n\end{array}\right|$ is a skew-symmetric matrix then which of the following is equal to x+y+z?

• A. $a+b+c$
• B. $l+m+n$
• C. $-b-m$
• D. $c-l-n$

Answer 1

The correct option is C $-b-m$

if $A$ is a skew symmetric matrix, then $A^T=-A$
Now, $A^T=\left|\begin{array}{ccc}a& x& l\\ b& y& m\\ c& z& n\end{array}\right|$
So, $A^T=-A$
$=>\left|\begin{array}{ccc}a& x& l\\ b& y& m\\ c& z& n\end{array}\right|=\left|\begin{array}{ccc}-a& -b& -c\\ -x& -y& -z\\ -l& -m& -n\end{array}\right|$
$=>x=-b;y=-y$ or $y=0;z=-m$
So, $x+y+z=-b+0-m=-b-m$