The block diagram of a linear time invariant system is given in the figure is
- Write down the state variable equations for the system in matrix form assuming the state vector to be $\left[x_{1}(t) x_{2}(t)\right]^{\mathrm{T}}$
- Find out the state transition matrix.
- Determine $y(t), t \geq 0$, When the initial values of the state at time $t=0$ are $x_{1}(0)=1$, and $x_{2}(0)=1.$