Problem 3 You are given the following system of equations: -5x2 + x2 + 10x3 = 40 5x4 x2 X3 = 2 4x4 + 9x2 + 2x, = 33 a. What are the rank and the condition number of the coefficient matrix for the system? b. If justified, solve the system of equations by pre-multiplying the vector of constants by the inverse of the coefficient matrix (or by applying the backslash operator) c. Solve the system of equations using LU decomposition d. Solve the system of equations using the Jacobi method until the percent estimated relative error falls below 0.01%. Use zeros as initial values. If necessary, re-arrange the equations to achieve convergence. e. Repeat d) using the Gauss-Seidel method. Did the Gauss-Seidel method perform faster than the Jacobi method? Problem 3 You are given the following system of equations: -5x2 + x2 + 10x3 = 40 5x4 x2 X3 = 2 4x4 + 9x2 + 2x, = 33 a. What are the rank and the condition number of the coefficient matrix for the system? b. If justified, solve the system of equations by pre-multiplying the vector of constants by the inverse of the coefficient matrix (or by applying the backslash operator) c. Solve the system of equations using LU decomposition d. Solve the system of equations using the Jacobi method until the percent estimated relative error falls below 0.01%. Use zeros as initial values. If necessary, re-arrange the equations to achieve convergence. e. Repeat d) using the Gauss-Seidel method. Did the Gauss-Seidel method perform faster than the Jacobi method