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###### Problem 6_ The polynomials Ho (x) =1 Hi(x) = 2x Hz (x) = 4x2 _ 2 Hz(x) = 8x3 12x are called the Hermite polynomials. Show H {Ho (x), Hi (x), Hz(x), Hz(x)} is a basis for Qs'Problem 7. Using Problem 6, find each of the following: [1]#, [x]#, [x2]u, and [x?]x.Problem 8. Using your answer in Problem 7, create a 4 X 4 matrix A where each column is one of the vectors from your solution. Find A-1 (use a computer!) Compare this to the matrix you used in Problem 6. Briefly explain what you see, and

Problem 6_ The polynomials Ho (x) =1 Hi(x) = 2x Hz (x) = 4x2 _ 2 Hz(x) = 8x3 12x are called the Hermite polynomials. Show H {Ho (x), Hi (x), Hz(x), Hz(x)} is a basis for Qs' Problem 7. Using Problem 6, find each of the following: [1]#, [x]#, [x2]u, and [x?]x. Problem 8. Using your answer in Problem 7, create a 4 X 4 matrix A where each column is one of the vectors from your solution. Find A-1 (use a computer!) Compare this to the matrix you used in Problem 6. Briefly explain what you see, and why you think it happened:

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