Consider the following three sets of equations.
a) Write all of the above sets of equations in the matrix format and identify the sets that you cannot solve by using an iterative method such as Jacobi and/or Gauss-Seidel method. Show the details of how you decide that the method will not converge for the identified set.
b) If there is any set in the above three that will converge, select that (or any one if more than one exists) and manually show as many steps as you need for the Jacobi Method to achieve an absolute approximate relative error level for each variable below 5%.
c) Using the same set of equations that you used in b), manually show as many steps as you need for the Gauss-Seidel method to obtain the absolute approximate relative error level for each variable below 5%. While following Gauss-Seidel method steps, describe where you are doing different from that you did in case of the Jacobi method.
d) Consider the number of steps required in Jacobi Method and in Gauss-Seidel method to achieve the same quality (in terms of absolute approximate relative error to be below 5%) solutions. Which method is more efficient in the number of steps? Can you explain why that method is more efficient than the other?