i appreciate your help. The Hilbert matrices H(n) arise in finding polynomial ap

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appreciate your help.

The Hilbert matrices H(n) arise in finding polynomial approximations to functions defined on the unit interval. For example, when approximating the function sin(phix) on [O.1], the coefficients of the polynomial p(x) of degree n-1 that minimizes the squared error [sin(phix)-p(x)]2 dx, are solutions of the matrix equation H(n) c = b Using the following teclmiques explore the beliavior of the solutions to (1) for values of n up to 25: using basic Gaussian elimination using Gaussian elimination with (partially) scaled partial pivoting using LU factorization using Gauss - Seidel iteration in each case compute the residual eiror vector r = b - H(n)-c. compare your results for the three methods.

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you have to use matlab for this i am uploading matlab code with some comments

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