Originally Posted by
Morgan Find an orthonormal basis for the vector subspace of $\displaystyle \mathbb R^3,\,\mathbb W=\{(x,y,z)\in\mathbb R^3|x+y+z=0\}.$
Sketch of work:
i'll take $\displaystyle x=-y-z,$ so we have that
$\displaystyle \mathbb W=\{(-y-z,y,z)\in\mathbb R^3,\,\forall\,y,z\in\mathbb R\},$ thus $\displaystyle \mathbb W=\langle(-1,1,0),(-1,0,1)\rangle.$
these are linearly independent, so i have a basis for $\displaystyle \mathbb W$ which is $\displaystyle B_{\mathbb W}=\{(-1,1,0),(-1,0,1)\}.$
well, here's where i dunno what to do, don't know how to get the orthonormal basis for the subspace.