Exercise 5. Consider the vector space P3 with inner product defined by (f,g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) + f(2)g(2). (a) Find an orthonormal…
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Can anyone help me out with his problem? It is about Applied Linear Algebra.
Exercise 5.Consider the vector space P3 with inner product defined by(f,g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) + f(2)g(2).(a) Find an orthonormal basis for the subspace spanned by 1, x, and x2.(b) Find the projection of the function 1 + 4x onto the space P2.(c) Solve (a) and (b) when the inner product is defined by(f, g) = / f(x)g(x)dx.-1
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