(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How do I know if this linear transformation is invertible or not?

T: [ x ] ---> [ 2y ]

[ y ] [ x-3y ]

(I also uploaded a small .bmp file to represent this if this looks too ugly)

3. The attempt at a solution

Well, I thought maybe it could be represented by a transformation matrix T

[ 0 2 ]

[ 1 -3 ]

So then I just took the inverse of T, which I got as

[ 1.5 1 ]

[ 0.5 0 ]

So does that mean that in the question, it is invertible? Because if it is, I'm getting the impression that these R^{2}to R^{2}linear transformations are invertible. Would this impression be correct?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Matrices and Invertible Linear Transformations

**Physics Forums | Science Articles, Homework Help, Discussion**