Consider a linear system whose state space representation is ˙x(t)=Ax(t).If the initial state vector of the system is x(0)=[1−2],then the system response is x(t)=[e−2t−2e−2t]. If the initial state vector of the system changes to x(0)=[1−1], then the system response becomes x(t)=[e−t−e−t].The eigen-value and eigen-vector pairs (λi,vi) for the system are

Consider a linear system whose state space representation is ˙x(t)=Ax

1.	Consider a linear system whose state space representation is ˙x(t)=Ax(t).If the initial state vector of the system is x(0)=[1−2],then the system response is x(t)=[e−2t−2e−2t]. If the initial state vector of the system changes to x(0)=[1−1], then the system response becomes x(t)=[e−t−e−t].The eigen-value and eigen-vector pairs (λi,vi) for the system are
Answer» Consider a linear system whose state space representation is $˙ x (t) = A x (t) .$ If the initial state vector of the system is $x (0) = [\begin{matrix} 1 - 2 \end{matrix}]$ ,then the system response is $x (t) = [\begin{matrix} e^{- 2 t} - 2 e^{- 2 t} \end{matrix}] .$ If the initial state vector of the system changes to $x (0) = [\begin{matrix} 1 - 1 \end{matrix}],$ then the system response becomes $x (t) = [\begin{matrix} e^{- t} - e^{- t} \end{matrix}] .$ The eigen-value and eigen-vector pairs $(λ_{i}, v_{i})$ for the system are