Question: 6) Consider the real vector space V = {ax + b|a, b R} equipped with the inner product f,g = 0 1 f ( x

6) Consider the real vector space V = {ax + b|a, b R} equipped with the inner product

f,g = 01f(x)g(x)dx f,g V.

Let B be the subset { 3^1/2x,3x-2} of V.

(a) Show that B is an orthonormal basis of V.

(b) Find the coordinate of 1 with respect to the basis B.

6) Consider the real vector space V = {ax + b|a, b

6. Consider the real vector space V = {ax + bla, b E R} equipped with the inner product (f,g) = f(x)g(x)dx f,g EV. Let B be the subset { V3x, 3x -2} of V. (a) Show that B is an orthonormal basis of V. (b) Find the coordinate of 1 with respect to the basis B

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