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| + | If W(t)=Z(t) then it is linear | ||
| + | ===Non-Linear System=== | ||
| + | take <math>\,\ x(t) = 3t^2, y(t) = t^3</math> | ||
| + | |||
| + | and <math>\,\ a = 2, b = 3</math> | ||
| + | |||
| + | The system squares the function that goes in. | ||
| + | |||
| + | Then we get | ||
| + | |||
| + | <math>\,\ Z(t) = 2t^4 + 3t^6 </math> and | ||
| + | |||
| + | <math>\,\ W(t)= (2t^2+3t^3)^2 </math> | ||
| + | |||
| + | we see that Z(t) and W(t) are not equal so they are not linear. | ||
| + | ===Linear System=== | ||
| + | I am taking the same values except now the system just multiplies it by 4. | ||
| + | |||
| + | <math>\,\ Z(t) = 8t^2 + 12t^3 </math> and | ||
| + | |||
| + | <math>\,\ W(t)= 4(2t^2+3t^3) </math> | ||
| + | |||
| + | and '''BAM''' we get a linear function because Z(t)=W(t) | ||
Revision as of 18:03, 11 September 2008
Not Words But Diagrams
If W(t)=Z(t) then it is linear
Non-Linear System
take $ \,\ x(t) = 3t^2, y(t) = t^3 $
and $ \,\ a = 2, b = 3 $
The system squares the function that goes in.
Then we get
$ \,\ Z(t) = 2t^4 + 3t^6 $ and
$ \,\ W(t)= (2t^2+3t^3)^2 $
we see that Z(t) and W(t) are not equal so they are not linear.
Linear System
I am taking the same values except now the system just multiplies it by 4.
$ \,\ Z(t) = 8t^2 + 12t^3 $ and
$ \,\ W(t)= 4(2t^2+3t^3) $
and BAM we get a linear function because Z(t)=W(t)
