Finding the missing vector such that the matrix is orthonormal

g.lemaitre

1. The problem statement, all variables and given/known data
A matrix is orthonormal if the magnitude of its vectors = 1 and all vector pairs are perpendicular, that is, their dot product = 0. Find the missing vector which would make the following matrix orthonormal:
[tex]
\begin{bmatrix}
\frac{1}{\sqrt{5}} & x \\
\frac{2}{\sqrt{5}} & y \\
\end{bmatrix}[/tex]
Most textbooks use [tex] x_1 and x_2[/tex] but I find x and y easier
2. Relevant equations
3. The attempt at a solution
[tex]
\frac{1}{\sqrt{5}}x + \frac{2}{\sqrt{5}} = 0 ... space here ...
\sqrt{x^2 + y^2} = 1
[/tex]
I tried setting x = y and I got
[tex]
\frac{1}{\sqrt{5}}x = -\frac{2}{\sqrt{5}}[/tex]
But that's as far as I could with that problem.

g.lemaitre

I solved this problem.

g.lemaitre

I've solved this problem.