Write the code in MATLAB please

6 Eigenvalue/Eigenvector Problems (I) 1. Write Maple and/or Matlab code that implements the Faddeev-Leverrier method seen in class. Use your code to compute the characteristic polynomial of the Hilbert matrix H5 by the Faddeev-Leverrier method. Compare your results with the characteristic polynomial as computed by built-in Maple or Matlab commands. 2. Prove that H5 has five positive eigenvalues. Denote these eigenvalues by 1,2,3, 4,5. Find numerical values for i,i=1,,5 by using a numerical method of your choice (from the ones seen in class) to solve the characteristic polynomial. Use the numerical values you found for i to verify numerically that i=15i=563/315 and that i=15i=1/266716800000 3. Prove that H5 is a positive-definite matrix. 4. Since H5 is symmetric and positive-definite, it possesses a Cholesky decomposition H5=LLT. Compute the lower triangular matrix L by writing L=l11l21l31l41l510l22l32l42l5200l33l43l53000l44l540000l55 and subsequently performing the multiplication LLT and equating the elements of the resulting matrix with the corresponding elements of H5. Compare your result with the result found by built-in Maple or Matlab commands. 5. Solve the following five systems of linear equations: Hkx=1,k=6,7,8,9,10, where 1 is the k1 column vector whose all k entries are equal to 1 , for k= 6,7,8,9,10. Examine the solutions closely and mention any kind of patterns that you may notice. If you noticed any pattern in the question above, can you prove that this pattern will in fact occur for every k