Linear algebra help

1. Oct 23, 2009

esler21

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

2. Relevant equations

3. The attempt at a solution

2. Oct 23, 2009

Delphi51

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

3. Oct 23, 2009

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.