Given this tridiagonal system: [4 -1 0 0 0 0 100 -1 4 -1 0 0 0 200 0 -1 4 -1 0 0 200 0 0 -1 4 -1 0 200 0 0 0 -1 4 -1 200 0 0 0 0 -1 4 100]. a. Solve the system using the algorithm for a compacted system matrix that has n rows but only four columns. b. How many arithmetic operations are needed to solve a tridiagonal system of n equations in this compacted arrangement? How does this compare to solving such a system with Gaussian elimination without compacting? Derive an algorithm and write an MATLAB program to solve a linear system Ax = b, where A is an N times N band matrix with bandwidth W. You can generalize the algorithm you develop in Exercise 35 to handle a band matrix. The system of Exercise 34 is an example of a symmetric matrix. Because the elements at opposite positions across the diagonal are exactly the same, it can be stored as a matrix with n rows but only three columns. a. Write an algorithm for solving a symmetric tridiagonal system that lakes advantage of such compacting. b. Use the algorithm from part (a) to solve the system in Exercise 34. c. How many arithmetic operations are needed with this algorithm for a system of n equations