Linear Algebra Help: Is L:R^2 -> R^2 a Linear Transformation?

[esler21]

Is L:R^2 - ->R^2 defined by L(x,y) = (x-1,y-x) a linear transformation? Explain why or why not.

Homework Equations

The Attempt at a Solution

 

[Delphi51]

esler, I suggest you take this one over to the math section of the forum.

 

[VeeEight]

Apply the properties of a linear transformation:
http://en.wikipedia.org/wiki/Linear_map#Definition_and_first_consequences

There are two properties to verify, as outlined in the link. For the first one, take two arbitrary elements of R², you can call them (x₁, y₁) and (x₂, y₂), and see if they satisfy the first property. You may use the usual point wise addition for the ordered pairs.
Then take an arbitrary scalar to see if the second property is satisfied.

You might also find this page useful:
http://ltcconline.net/greenl/courses/203/Vectors/linearTransRn.htm