Use Matlab to do it

4.14. (a) The matrix exponential function of an n x n matrix A is defined by the infinite series 3 AP exp(A) = I + A+ + 2! 3! Write a program to evaluate exp(A) using the foregoing series definition. (b) An alternative way to compute the matrix ex- ponential uses the eigenvalue-eigenvector decom- position A = U diag(41, ..., In)U-1, where 11, ...,In are the eigenvalues of A and U is a matrix whose columns are corresponding eigen- vectors. Then the matrix exponential is given by exp(A) = U diag(e{1, ..., en)U-1. Write a second program to evaluate exp(A) using this method. Test both methods using each of the following test matrices: 2 A1 -1 2 -1 A2 -49 24 -64 31 1] Compare your results with those for a library rou- tine for computing the matrix exponential. Which of your two routines is more accurate and robust? Try to explain why. See (333, 334] for several ad- ditional methods for computing the matrix expo- nential