Math 54 quiz 8 compute an orthogonal basis of p2 where the

Question

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

3. Find all least squares solutions to Ax = b where A = and b =

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.