Linearity Rules for Proving Non-Linearity

Thread starter shutoutsteve
Start date Nov 4, 2008
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Linearity Rules

AI Thread Summary

Linearity rules for proving non-linearity focus on the condition that a function f is linear if it satisfies f(x+y) = f(x) + f(y) and f(cx) = cf(x) for all scalars c. The discussion highlights the need for clear resources, as the textbook and professor are not providing adequate guidance. Specific examples of functions to analyze for linearity include f(x) = (|x1|, |x2|), f(x) = (1, 2) + 3x, and f(x) = (0, 1). Understanding these principles is crucial for solving "prove this is not linear" questions effectively. Access to straightforward links or resources on linearity rules is requested to aid in comprehension.

Nov 4, 2008

shutoutsteve

Does anyone have a straightforward link to linearity rules? My textbook is not very helpful and my prof never knows what he is talking about :(.
I have a few "prove this is not linear" questions to do
f(x)=(|x1|,|x2|)
f(x)=(1,2)+3x
f(x)=(0,1)

I should know this, but i tend to forget the silly little things.
:(

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Nov 4, 2008

nealh149

Basically a function is linear if f(x+y) = f(x) + f(y)

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