Use the dot product in R" unless otherwise instructed.
In each case, verify that B is an orthogonal basis of V with the given inner product and use the expansion theorem to express v as a linear combination of the basis vectors
(a)

(b)

V = R3, (v, w) = VTAw where A =

(c) v = a + bx + cx2, B = {1, x, 2 - 3x2}, V = P2, (P, q) = P(0)q(0) + p(l)q(l) + p(-1)q( -1)
(d)

Transcribed Image Text:

V-R (v,w) = vAw where AE: 2 5 161 ab 201 1 0 2 o-1L-10