Final answer:
The given state-space representation represents a system in physics. To solve the differential equation, find the eigenvalues and eigenvectors of the coefficient matrix and calculate the corresponding solution.
Step-by-step explanation:
The given state-space representation represents a system in physics. State-space representation is a mathematical model used to describe the behavior of a system over time. In this case, the system is described by the differential equation dX(t)/dt = [0 -1] [2 -2].
To solve the differential equation, we can find the eigenvalues and eigenvectors of the coefficient matrix [2 -2] and calculate the corresponding solution. The eigenvalues of the matrix are λ₁ = 1 and λ₂ = -1, and the corresponding eigenvectors are v₁ = [1 1] and v₂ = [-1 2] respectively.
The general solution for the system is X(t) = c₁e^(λ₁t)v₁ + c₂e^(λ₂t)v₂, where c₁ and c₂ are constants determined by the initial conditions. The exact solution depends on the initial conditions provided.