(a) Use (1) to find the general solution ofUse a

(a) Use (1) to find the general solution of

Use a CAS to find e^At. Then use the computer to find eigenvalues and eigenvectors of the coefficient matrix

and form the general solution in the manner of Section 8.2. Finally, reconcile the two forms of the general solution of the system.

(b) Use (1) to find the general solution of

Use a CAS to find eAt. In the case of complex output, utilize the software to do the simplification; for example, in Mathematica, if m = MatrixExp[A t] has complex entries, then try the command Simplify[ComplexExpand[m]].