We would like to solve the differential equation \frac{d \boldsymbol{u}}{d t}=A \boldsymbol{u} \quad \text { with } \quad A=\left[\begin{array}{lll}

1 & 2 & 3 \\

2 & 2 & 2 \\

3 & 2 & 1

\end{array}\right] \quad \text { with } \quad \boldsymbol{u}(0)=(1,0,0) (a) Why is it guaranteed that A is diagonalizable? (b) Diagonalize A. (c) Using the diagonalization of A, solve for u(t).