Finding orthogonal basis for the nullspace of a matrix?

[cookiesyum]

Homework Statement

Find an orthogonal basis for the nullspace of the matrix

[2 -2 14]
[0 3 -7]
[0 0 2]

Homework Equations

The Attempt at a Solution

The nullspace is x = [0, 0, 0], so what is the orthogonal basis? It can be anything can't it?

 

[Mark44]

The nullspace (or kernel) of this matrix is {(0, 0, 0)}. The zero vector is the only vector in this set, so you're done.