Finding the missing vector such that the matrix is orthonormalby g.lemaitre Tags: matrix, missing, orthonormal, vector 

#1
Jul2712, 03:08 AM

P: 274

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
Jul2712, 03:29 AM

P: 274

I solved this problem.




#3
Jul2712, 03:32 AM

P: 274

I've solved this problem.



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