(→Linear System Example) |
(→Linear System Example) |
||
| Line 14: | Line 14: | ||
Consider the system | Consider the system | ||
<math> \mathbf{a}\cdot\mathbf{M}=\mathbf{b} </math> | <math> \mathbf{a}\cdot\mathbf{M}=\mathbf{b} </math> | ||
| − | where <math> \mathbf{M} = \begin{bmatrix}1 & 2 \\ 3 & 4 \\ \end{bmatrix} </math> | + | where |
| − | + | <math> \mathbf{a} = \begin{bmatrix}4 & 1 \end{bmatrix} </math>, | |
| − | + | <math> \mathbf{M} = \begin{bmatrix}1 & 2 \\ 3 & 4 \\ \end{bmatrix} </math>, | |
| − | + | and <math> \mathbf{b} = \begin{bmatrix}7 & 12 \end{bmatrix} </math> | |
Revision as of 10:05, 10 September 2008
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{a} = \begin{bmatrix}4 & 1 \end{bmatrix} $, $ \mathbf{M} = \begin{bmatrix}1 & 2 \\ 3 & 4 \\ \end{bmatrix} $, and $ \mathbf{b} = \begin{bmatrix}7 & 12 \end{bmatrix} $
