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**[SOLVED] Vectors that form bases (linear algebra)**

## Homework Statement

I am given two vectors u and v, which are:

u = (1/2 , 1/2 , 1/2 , 1/2) and

v = (1/2 , 1/2 , -1/2 , -1/2).

I have to find an orthonormal basis for R^4 containing u and v.

## The Attempt at a Solution

The first thing that came to me was Gram-Schmidt - but then I saw that the dot-product between u and v is zero, so Gram-Schmidt is overkill.

I just need to find two other linearly independant vectors that has dot-product equal zero with respectively u and v. Is that even possible and how would I do that?