# MA428 HW1 - this but everyone should hand in their own...

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Homework 1. Due February 7. You can get a maximum of 10 points on this problem, one for each correct digit in your answer. This problem demonstrates the limitations of Gaussian elimination on a relatively simple problem. Compute the largest in magnitude entry of H -1 , where H is the 100-by-100 matrix H ij =1/(i+j). i,j=1,2,...,100. You may use any tools and software you like. You may collaborate on
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Unformatted text preview: this, but everyone should hand in their own solution. (Hint: The determinant of the matrix C(i,j)=1/(x i +y j ) is det C = [\prod i< j (x j-x i )(y j-y i )]/ [\prod i,j (x i +y j )]. Any submatrix of a C has the same form. You can use Cramer's rule in order to compute accurate formulas for the entries of H-1 ....
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