A General Demonstration of the Linearity of Zero-State, Zero-Input and Steady-State Responses

The demonstration includes two steps. Firstly, the linear relationship between zero-state and zero-input responses of linear networks is demonstraped Then the linear relationship of steady state response is discussed. In the course of demonstration, several theorems are posed and proved in detail, such as networks including pure capacitance cut-sets and pure inductance loops are non-decaying, etc.