The total number of matrices A=pmatrix0&2y&12x&y&-12x&-y&1pmatrix (x,yR, x y) for which A^…

Question

The total number of matrices $A=\begin{pmatrix}0&2y&1\2x&y&-1\2x&-y&1\end{pmatrix}$ ($x,y\in\mathbb{R},\ x
e y$) for which $A^TA=3I_3$, is:

Accepted Answer

Computing $A^TA=3I_3$ and reading off the diagonal entries gives $8x^2=3$ and $6y^2=3$, so $x=\pm\sqrt{3/8},\ y=\pm\sqrt{1/2}$.

Each has $2$ independent sign choices (and $x
e y$ is automatically satisfied), giving $2	imes2=4$ combinations.

Solutions · 1