(Solved): Matching Drop down Menu. Instructions: Select the items from the drop-down menu below to match the ...

Matching Drop down Menu. Instructions: Select the items from the drop-down menu below to match the items on the left column A continuous-time LTI system at rest is given by its State and Output Equations, $$\begin{array}{c}\left[\begin{array}{l}\stackrel{?}{x_1}\\ \stackrel{?}{x_2}\end{array}\right]=\left[\begin{array}{cc}0& 1\\ ?2& ?3\end{array}\right]\left[\begin{array}{l}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{l}0\\ 1\end{array}\right]u_{in}\\ y=\left[\begin{array}{ll}1& 0\end{array}\right]\left[\begin{array}{l}{x}_1\\ x_2\end{array}\right]\end{array}$$ The Laplace Transform of the State Response to a unit-step; $$\left({\mathbf{u}}_{\text{in }}(\mathbf{t})=\mathbf{u}(\mathbf{t})\right)$$, can be given as (calculate $$\mathbf{a},\mathbf{b},\mathbf{c},\mathbf{d},\mathbf{e}$$ ), $$X(s)=\left[\begin{array}{c}\frac{a}{s}+\frac{\mathbf{b}}{s+1}+\frac{\mathbf{c}}{s+2}\\ \frac{\mathbf{d}}{s+1}+\frac{\mathbf{e}}{s+2}\end{array}\right]$$