Question: Exercise Suppose we wish to find the best quadratic function fitting the points (0, 1), (1, 0), (2, 1.5), (3, 4), (4, 8). Bo (a)

Exercise Suppose we wish to find the best quadratic function fitting the points (0, 1), (1, 0), (2, 1.5), (3, 4), (4, 8). Bo (a) Set up a linear system Ax = b describe the coefficients x = BI B2 (b) Find the singular value decomposition of A. (c) What is the rank r of A? (d) Define U, to be the first r columns of U, V, to be the first r columns of V, and E, to be a square r x r diagonal matrix. Use Sage to verify that A = U,E,VT. (e) Then the least squares approximation of the equation Ax = b is given by x = V,E,'U,b

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