1. Central difference approximation In the example project, I tested the forward difference approximation method for derivatives. There is also a "central difference" formula. Your task is to perform similar testing using the central difference formula. Also please determine if your results depend on the test function you use (instead of sin(x) ). Discuss your results. 2. Effect of pivoting Modify my gaussj function (and give it a new name) to perform the simpler Gauss-Jordan elimination without pivoting. Write Matlab code to determine how the accuracy and computation time of both versions depends on problem size. Discuss your results. 3. Near-singular matrices Determine how accurate Gauss-Jordan elimination is when applied to a near-singular matrix. Here is a suggested approach. Create a random NxN matrix and make it near-singular by replacing the last row by the second-last row, plus some small random numbers: A(end,:)=A(end1,:)+prand(1,N); p controls how large the added random numbers are. Make p small enough and N large enough to make the results of this problem interesting. Solve the problem with Gauss-Jordan, and also by Matlab's builtin solver: x=Ab; Compare results from the two solvers, and discuss. 4. Gaussian elimination with backsubstitution Write a function "gaussb" for Gaussian elimination with backsubstitution (see textbook for a more detailed explanation). Use partial pivoting as was done in gaussj. Test your code on one test problem and show that the residuals are close to zero