let
p(x) = a0 + a1x + a2x2 and q(x) = b0 + b1x + b2x2
be vectors in p2 with
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p, q
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= a0b0 + a1b1 + a2b2.
determine whether the polynomials form an orthonormal set, and if not, apply the gram-schmidt orthonormalization process to form an orthonormal set. (if the set is orthonormal, enter orthonormal in both answer blanks.)
{? 2 + x2, ? 2 + x}