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)
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