Solve the initial value problem $d\frac{x}{d}t=Ax$ with $x(0)=x_0.$

$A=\left[\begin{array}{ccc}4& -2& 1\end{array}\right]$

$3,x_0=\left[\begin{array}{c}0\end{array}\right]$

$1$

$x(t)=[\frac{e^{\frac{5t}{2}}[-\frac{4}{15}sin(\frac{15}{2}t)]}{\frac{11}{2}{e}^{-5t}+\frac{1}{2}{e}^{-6t^2}},x]$