Question

If $A=\frac{1}{3}\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& -2\\ x& 2& y\end{array}\right]$ is an orthogonal matrix then value of x+y is equal to

• A. -3
• B. \N
• C. 1
• D. 3

Answer 1

The correct option is A -3

$A.A^T=I\Rightarrow \frac{1}{9}\left[\begin{array}{ccc}9& 0& x+4+2y\\ 0& 9& 2x+2-2y\\ x+4+2y& 2x+2-2y& x^2+y^2+4\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$
$x+4+2y=0,2x+2-2y=0\Rightarrow x=-2,y=-1$