Chapter 9.8, Problem 10E

In Problems 7-10, determine $e^{At}$ by first finding a fundamental matrix $X\left(t\right)$ for $x^{\prime }=Ax$ and then using formula (3)

$A=\left[\begin{array}{ccc}0& 2& 2\\ 2& 0& 2\\ 2& 2& 0\end{array}\right]$