Very simple linear algebra question:

[frasifrasi]

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.

 

[eok20]

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?

 

[HallsofIvy]

In particular, look at what happens to y₂.

 

[frasifrasi]

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?