Question

If $A=\left(\begin{array}{ccc}x& 1& 4\\ -1& 0& 7\\ -4& -7& 0\end{array}\right)$ such that $A^T=-A$, then $x=$

• A. $-1$
• B. $0$
• C. $1$
• D. $4$

Answer 1

Answer: (B)

$0$

Given $A=\left(\begin{array}{ccc}x& 1& 4\\ -1& 0& 7\\ -4& -7& 0\end{array}\right)$
and $A^T=-A$
So By property of traspose (I), and opertaion of matrixes (4),
$A^T=\left(\begin{array}{ccc}x& -1& -4\\ 1& 0& -7\\ 4& 7& 0\end{array}\right)=-A=\left(\begin{array}{ccc}-x& -1& -4\\ 1& 0& -7\\ 4& 7& 0\end{array}\right)$
So, By equality of matrixes,
$x=-x$
$\Rightarrow x=0$