Consider the functions p 1 (x) = (x - 2) 2 - 2 and p 2 (x)
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Consider the functions p1(x) = (x - 2)2 - 2 and p2(x) = -x + 1. The inner product is defined for two functions f and g as (f,g) =0f(x)g(x)exp(x)dx
(a) Demonstrate that p1 and p2 are orthogonal w.r.t. the inner product as defined above.
(b) The function g(x) = (- 9x2 - 11 + 29x) is a function in the span of p1 and p2. Express g(x) as a linear combination of p1(x) and p2(x).
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