(a) Create a 3 x 3 Hilbert matrix. This will be your matrix [A]. Multiply the matrix by the column vector {x} = [1, 1, 1]T. The solution of [A] {x} will be another column vector {b}. Using any numerical package and Gauss elimination, find the solution to [A]{x} = {b} using the Hilbert matrix and vector {b} that you calculated. Compare the result to your known {x} vector. Use sufficient precision in displayed results to allow you to detect imprecision.

(b) Repeat part (a) using a 7 x 7 Hilbert matrix.

(c) Repeat part (a) using a 10 x 10 Hilbert matrix.