MATH 54 QUIZ 8-
1. True/False? Justify your answer. If ||u - v||2 = ||u||2 + ||v||2, then u is orthgonal to v.
2. Find the orthogonal projection of b =
onto W = Span ![2082_Figure1.png](https://secure.tutorsglobe.com/CMSImages/2082_Figure1.png)
3. Find all least squares solutions to Ax = b where A =
and b = ![158_Figure3.png](https://secure.tutorsglobe.com/CMSImages/158_Figure3.png)
4. Compute an orthogonal basis of P2 where the inner product is defined by
(f, g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) .
5. Let A and B be n × n orthogonal matrices. Show that AB is orthogonal.