Linearity Rules for Proving Non-Linearity: A Guide

[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.
:(

 

[nealh149]

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

 

[thomate1]

As a scientist, it is important to have a solid understanding of the principles and rules that govern linearity. While textbooks and professors can provide guidance, it can also be helpful to seek additional resources.

One straightforward link to linearity rules can be found on the website of the National Institute of Standards and Technology (NIST). They have a comprehensive guide on linearity and its rules, which can be accessed at https://www.nist.gov/calibrations/linearity.

In regards to your specific "prove this is not linear" questions, I would suggest reviewing the definition of linearity and its key properties. For example, a function is considered linear if it follows the properties of superposition and homogeneity. Can you identify any violations of these properties in the given functions?

It is also important to remember that linearity is not always a straightforward concept and there can be exceptions and gray areas. It may be helpful to consult with your professor or classmates for clarification on any confusing aspects. Additionally, practicing and reviewing similar problems can help solidify your understanding of linearity rules.

Overall, it is important to have a strong understanding of linearity in order to accurately analyze and interpret data in scientific research. I encourage you to continue seeking resources and practicing to improve your understanding of linearity rules.