Linear operator from matrix to general presentaition Let  $T:\mathbb{R}^{3}\rightarrow \mathbb{R}^{3}$ be a linear operator defined by:
$T(0,1,1)=(2,-1,1), T(2,-1,0)=(1,1,0), T(-1,0,0)=(1,-1,1)$.
I need to find $T(x,y,z)$. 
First of, i have found $[T]_{A}^{B}$ where A is the origin vectors and B is the image vectors that A is sent to.
I computed it to be
$$[T]_A^B=\begin{pmatrix} 1 & 0 & 2 \\
2 & - 1& 2 \\
2 & -3 & 3 \end{pmatrix}$$
But now after I have that matrix I am kind of lost. Is that even the right way to start?

Hint: Notice that $(0,1,1)$, $(2,-1,0)$, and $(-1,0,0)$ form a linearly independent set. On top of that, $(2,-1,1)$, $(1,1,0)$, and $(1,-1,1)$ form a linearly independent set. That means you already know $T$ with respect to the first basis (first set of vectors I wrote), and you know that it maps to another linearly independent set.
