Let T : P2 → P2 be the linear transformation defined by
T(a + bx + cx2) = 3a - cx2:
Let f = f(x) = 1 + x.
(a) Assuming that P2 has the inner product defined as
?a + bx + cx2; d + ex + fx2? = ad + be + cf;
find all vectors q = q(x) ∈ P2 such that
?f; q? = ?T(f); T(q)?:
(b) Assuming that P2 has the inner product defined as
?f(x); g(x)? = f(-1)g(-1) + f(0)g(0) + f(1)g(1);
find all vectors q = q(x) ∈ P2 such that
?f; q? = ?T(f); T(q)?: