Linear System Definition
A system takes a given input and produces an output. For the system to be linear it must preserve addition and multiplication. In mathematical terms:
$ x(t+t0)=x(t) + x(t0) $
and
$ x(k*t)=k*x(t) $
Linear System Example
Consider the system $ \mathbf{a}\cdot\mathbf{M}=\mathbf{b} $ where $ \mathbf{M} = \begin{bmatrix}1 & 2 \\ 3 & 4 \\ \end{bmatrix} $ is the identity matrix, $ \mathbf{a} = \begin{bmatrix}4 & 1 \end{bmatrix} $
and y(t) and x(t) are n x 1 vectors. $ Insert formula here $
