Hello, this is my first time posting. I've been wracking my brain over the following problem for two days now and without any sort of examples in my book, study guide or notes I'm starting to go crazy.

Here's the problem: Let L: $\displaystyle R^2$ $\displaystyle \rightarrow$ $\displaystyle R^3$ such that:

L(1 -1) = (2 1 3) AND L(-2 3) = (-1 0 -1)

a) Determine Lx

b) Determine if L is one-to-one.

Now, I know if I can find what the transformation is, with the given information, I can tell if it's one-to-one without any problems but I, quite honestly, don't know where to begin on figuring out what the transformation is.

Thank you so much in advance!