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Question: problem 4 15 points a consider the space pi of...

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Problem 4 (15 points) a) Consider the space Pi of the polynomials of degree S 1 (e.g. 2,3+t,5+6,...), we define the inner product and induced norm, respectively, as (f, g) 팀 (/(0)9(0) + f(1)s(1)) Find an orthonormal basis for this inner product space that is NOT the standard basis nor a simple scalar multiple of the standard basis vectors (Hint: but something similar). b) Consider an invertible n x n matrix A whose columns are orthogonal, but not necessarily orthonormal. What does the QR factorization of A look like?

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