5. (10%) Find the inverse Laplace transform of F(s)

7. (20%) Assume we have collected the data from four types of sensors four times from two experiments. Put these data in the form of matrix A and B. Check if matrix A and matrix B are diagonalizable. If it is diagonalizable, compute a matrix P such that BP is a diagonal matrix and compute the determinant of A4-5A2+2I or B4-5B2+2I. I is an identity matrix.