(New page: = Linearity = A system is called linear if and only if: <math>f(ax_1 + bx_2) = af(x_1) + bf(x_2)</math>) |
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<math>f(ax_1 + bx_2) = af(x_1) + bf(x_2)</math> | <math>f(ax_1 + bx_2) = af(x_1) + bf(x_2)</math> | ||
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| + | == Example of a linear system == | ||
| + | System is: <math> f(x) = 23x<math> | ||
| + | <math>X_1(t) = t^2</math> | ||
| + | <math>X_2(t) = 2t^2</math> | ||
| + | |||
| + | <math>f(aX_1 + bX_2) = af(X_1) + bf(X_2)</math> | ||
| + | <math>f(at^2 + 2bt^2) = af(t^2) + bf(t^2)</math> | ||
| + | <math>f(at^2 + 2bt^2) = a*23t^2 + b*46t^2</math> | ||
| + | <math>f(at^2 + 2bt^2) = 23(at^2 + 2bt^2)</math> | ||
| + | <math> f(x) = 23x<math> | ||
| + | |||
| + | |||
| + | == Example of a non-linear system == | ||
Revision as of 17:12, 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<math> <math>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 == $
