Very simple linear algebra question:

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Homework Help Overview

The discussion revolves around a linear algebra question concerning the properties of a given linear transformation defined by specific equations. The original poster seeks clarification on why the transformation is not considered linear, citing a lack of examples in their textbook.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the criteria for linearity, specifically referencing the conditions that define a linear transformation. There is an exploration of the behavior of one of the transformation's components, y_2, and questions arise about how to apply the linearity criteria to this specific case.

Discussion Status

Some guidance has been offered regarding the definition of linear transformations, but the discussion remains open as participants continue to seek clarification on the application of these concepts to the specific transformation in question.

Contextual Notes

The original poster expresses uncertainty about the criteria for linearity and notes that their textbook lacks detailed examples, which may be contributing to their confusion.

frasifrasi
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This is a very basic question, but I am not understanding the concept here.

it asks, consider the linear transformation:

y_1(y subscript 1) = x_2 - x_3
y_2 = x_1*x_3
y_3 = x_1 - x_2

Can anyone explain why this is not linear? I am not sure what the criteria is and the book doesn't have any example like this reasoned out.

Thank you.
 
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A transformation T is linear if T(cv) = cT(v) and T(v+w) = T(v) + T(w) for all scalars c and vectors v and w. Does this help?
 
In particular, look at what happens to y2.
 
Ok, so for y_2:

x(x_1*x_3) is not the same as...?

I am not sure how to apply this. Can someone explain how to proceed?
 

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