5 Systems of Linear Equations 5.1 Gauss Elimination Write Maple and/or Matlab code to implement Gauss elimination, as seen in class. 5.2 Gauss-Jordan Eliminationn Write Maple and/or Matlab code to implement Gauss-Jordan elimination, as seen in class. 5.3 The Hilbert matrix The Hilbert matrix H,-(hy) is a square n n symmetric matrix with hi,-- - for i,j,,n. For example, for n = 5, the Hilbert matrix of order 5 5 is: 1 1/2 1/3 1/4 1/5 1/2 1/3 1/4 1/5 1/6 Hs1/3 1/4 1/5 1/6 1/7 1/4 1/5 1/6 1/7 1/8 1/5 1/6 1/7 1/8 1/9 1. Use your Gauss Elimination and Gauss-Jordan Elimination implementations to solve the following system of linear equations: where is the 5 x 1 column vector whose all 5 entries are equal to1 2. Use your implementation to compute the determinant of Hs, using Gauss elimina- tion. Compare your result with the determinant as computed by built-in Maple or Matlab commands 3. Use your implementation to compute the inverse matrix H using Gauss-Jordan elimination by appending the I identity matrix to Hs. Compare your result with the inverse matrix as computed by built-in Maple or Matlab commands. 4. Compute the condition number of Hs by the formula K(Hs) = 11H5ll-HGill, for two different norms: (1) the 1-norm (2) the Frobenius norm