4. Consider the same function f(x) = xe" again. Now, we are going to find the interpolating polynomial by using the Vandermonde matrix method: (a) Construct the Vandermonde matrix V if f(x) passes through the nodes -1, 0 and 1. (b) Compute: det(V). (c) Find the inverse matrix V-1. (d) The coefficients ao, a1, az of the interpolating polynomial p2(x) can be computed by using the equation A = V-1F, where the symbols have their usual meanings. Using V-1 and the function values at the nodal points, find the values of A up to five decimal places. (e) Write down the expression for p2(x). Also compute p2(0.25) and f(0.25) up to five decimal places. (f) Find the percent error of interpolating f(0.25) by pP2(0.25).

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