Compute the matrix exponential e At for each system x ' Ax given in Problems 9 through 20 x ' 1 13x 1 4x 2 , x ' 2 4x 1 7x 2 Data in Problem 9 through 20 9 x 5x14x2, x 2x1 x2 x 4x14x2 10 x 6x16x2, x 2 11 x 5x13x2, x 2x1 12 x 5x1 4x2, x 3x1 2x2 13 x 9x18x2, x 6x1 5x2 14 x 10x6x2, x 12x1 7x2 15 x6x11...

To compute the matrix exponential e At where A is the coefficient matrix of the system xAx we follow these steps Diagonalize matrix A if possible Compute e At using the diagonalized form of A if available To find the corresponding eigenvectors we substitute each eigenvalue back into AIX0 and solve for X We can express matrix A in terms of its eigenvectors and eigenvalues The diagonalization of A is given by Lets compute each part This is the matrix exponential for the given system If you have a specific value of t you can substitute it into this expression to get the numerical value of e At Given the system x ...