Register to reply 
Finding the missing vector such that the matrix is orthonormal 
Share this thread: 
#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.



Register to reply 
Related Discussions  
Orthonormal matrix  Calculus & Beyond Homework  3  
Matrix with Orthonormal columns  Linear & Abstract Algebra  5  
Finding an ODE given a vectormatrix  Calculus & Beyond Homework  0  
Orthonormal vector question..  Calculus & Beyond Homework  1  
A Matrix with Orthonormal Columns  Calculus & Beyond Homework  5 