(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Finding the missing vector such that the matrix is orthonormal

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