Chapter 7.2, Problem 9E

To determine

(a)

To write:

The system in the form $x^{\prime }\left(t\right)=Ax\left(t\right)$. Also, find one solution.

To determine

(b)

The vector $y_0$.

To determine

(c)

To prove:

The equation $y\left(t\right)=c_1{x}_1\left(t\right)+c_2{x}_2\left(t\right)$ satisfies $y(0)=x_0$ for any $x_0$ in $R^2$ for constants $c_1$ and $c_2$.