1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding the missing vector such that the matrix is orthonormal

  1. Jul 27, 2012 #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. Jul 27, 2012 #2
    I solved this problem.
     
  4. Jul 27, 2012 #3
    I've solved this problem.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook