How to Show a Function is Not a Linear Transformation  Summary and Q&A
TL;DR
A function in R^2 is shown to be nonlinear by providing an example that breaks the linearity condition.
Key Insights
 ❓ The linearity condition is an essential criterion to determine if a function is linear or not.
 👍 Finding just one example that breaks the linearity condition is sufficient to prove that a function is not linear.
 🈸 Calculations involving vectors and the function's application to them are necessary to compare the results and demonstrate linearity or nonlinearity.
 🥰 The provided example of v = [2, 3] and w = [3, 4] shows that the function is not linear.
Transcript
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Questions & Answers
Q: What is the definition of a linear function?
A linear function satisfies the condition that the function applied to the sum of two vectors equals the sum of the function applied to each vector separately.
Q: How can we prove a function is not linear?
To prove a function is not linear, we only need to find one example where the linearity condition does not hold true.
Q: What vectors are chosen as an example in this video?
The example chosen in the video includes the vectors v = [2, 3] and w = [3, 4].
Q: How is it shown that the function is not linear with the chosen example?
By calculating the function applied to v + w and comparing it to the sum of the function applied to v and w separately, it is shown that they are not equal.
Summary & Key Takeaways

The video discusses a given function in R^2 and aims to prove that it is not linear.

By applying the linearity condition to the function, an example is provided where it fails to hold true.

This example involves finding vectors, calculating the function applied to them, and comparing the results to disprove linearity.