Finding the missing vector such that the matrix is orthonormal

  1. 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.
     
  2. jcsd
  3. I solved this problem.
     
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