# Gram-Schmidt Transformation Process

Consider R3 with the Euclidean inner product.

Show that the vectors u = (1, 0, 0), v = (3, 7, −2), and w = (0, 4, 1) form a basis for R3, then use the Gram-Schmidt process to transform that basis into an orthonormal basis.

How would I use the Gram-Schmidt process to find an orthonormal basis with vectors u,v and w?

Any help would be appreciated.

• At least you could try to apply the process, which can easily be found in nearly every linear algebra textbooks... – Megadeth Dec 9 '15 at 5:03
• Once you obtain a set $\{ u', v', w' \}$ of orthogonal vectors from $\{ u,v,w \}$, the set $\{ u'/|u'|, v'/|v'|, w'/|w'| \}$ is orthonormal (why?). – Megadeth Dec 9 '15 at 5:05