# Linear transformation one-to-one

1. Oct 6, 2014

### jonroberts74

1. The problem statement, all variables and given/known data
let $T:\mathbb{R^3} \rightarrow \mathbb{R^3}$ where $T<x,y,z>=<x-2z,y+z,x+2y>$

Is T one-to-one and is the range of T $\mathbb{R^3}$?

3. The attempt at a solution

I took the standard matrix A $\left[\begin{array}{cc}1&0&-2\\0&1&1\\1&2&0\end{array}\right]$

det(A)=0 so by equivalence T is not one-to-one and by equivlence again the range is not $\mathbb{R^3}$

2. Oct 6, 2014

3. Oct 6, 2014

### jonroberts74

is that correct?

4. Oct 6, 2014