Orthogonally Diagonalizable

[john458776]

I have a little problem.

When I solve this problem I'm suppose to get the diagonal matrix that contain x : (10,1,1) diagonal.


When I do multiplication on the 2nd row, 3rd column I don't get zero I get something like square root of 10 over 10 on the diagonal matrix, I dont know if i made a mistake somewhere or what but I tried multiple times. I don't know what might be the problem.

 

[blamocur]

In case you are still interested in the solution, I am getting a pretty different diagonalizing matrix:
[math]U = \frac{1}{3\sqrt{5}} \left( \begin{array}{ccc} -2\sqrt{5} & -5 & 0 \\ 2\sqrt{5}& -4 & -3 \\ \sqrt{5} & -2 & 6 \end{array}\right)[/math]