Consider the inner product on P4, the vector space of polynomials of order up to 4, defined as (p(x), q(x)) = p(ao)q(ao) + · · · + p(a4)q(a4) ... with ao -2, a, = -1, a, = 0, az = 1 and as = 2. Using the polynomials Ili#k (x – a;) Il4k (ak – a;)' - SE(x) = k E {0,..,4}, where IIitk is the product over indices in {i E {0, . p(x) = x4 + x2 +1 in the form .., 4}|i # k}, express p(x) = ao 80(x) +… … +a484(x). ... With a precision of up to 3 decimal places, e.g. "4.598" or "6.667", calculate • the value of ao: • the value of 1: • the value of 2: • the value of az: • the value of a4:

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