| Line 6: | Line 6: | ||
== Example of a linear system == | == Example of a linear system == | ||
| − | System is: <math> f(x) = 23x \,<math> | + | System is: <math> f(x) = 23x \,</math> |
<math>X_1(t) = t^2 \,</math> | <math>X_1(t) = t^2 \,</math> | ||
<math>X_2(t) = 2t^2 \,</math> | <math>X_2(t) = 2t^2 \,</math> | ||
Revision as of 16:13, 10 September 2008
Linearity
A system is called linear if and only if:
$ f(ax_1 + bx_2) = af(x_1) + bf(x_2) $
Example of a linear system
System is: $ f(x) = 23x \, $ $ X_1(t) = t^2 \, $ $ X_2(t) = 2t^2 \, $
$ f(aX_1 + bX_2) = af(X_1) + bf(X_2) \, $ $ f(at^2 + 2bt^2) = af(t^2) + bf(t^2) \, $ $ f(at^2 + 2bt^2) = a*23t^2 + b*46t^2 \, $ $ f(at^2 + 2bt^2) = 23(at^2 + 2bt^2) \, $ $ f(x) = 23x \,<math> == Example of a non-linear system == $
