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.

  • 2
    $\begingroup$ At least you could try to apply the process, which can easily be found in nearly every linear algebra textbooks... $\endgroup$ – Megadeth Dec 9 '15 at 5:03
  • $\begingroup$ 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?). $\endgroup$ – Megadeth Dec 9 '15 at 5:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.