12 Ordinary Differential Equations IV

1. Solve the system
   
   $$\dot {\vec x} = A \vec x \quad \vec x(0) = \vec x_0 \qquad ... ...x_0 = \left( \begin{array}{c} 9 1 1 \end{array} \right)$$
   
   
   Use the nonmatrix exponential method. Give a fundamental matrix.

2. Solve the previous question, but this time use the matrix exponential method. Find $e^{At}$, then find the solution $\vec x$ as $e^{At}\vec x_0$ and check that it is the same as before.

3. Solve the system
   
   $$\dot {\vec x} = A \vec x + \vec g \quad \vec x(0) = \vec x... ...0 = \left( \begin{array}{c} 5 11 -2 \end{array} \right)$$
   
   
   Use the nonmatrix exponential method. Give a fundamental matrix.