can anyone help me get started with this question. Right now I am guessing and checking which is not efficient. I figured out out that the transformation is (?,?,x-y-z) so far
Let $T:\Bbb R^3\to \Bbb R^3$ be a linear transformation such that $T(1,1,1)=(2,0,-1)$, $T(0,-1,2)=(3,2,-1)$ and $T(1,0,1)=(1,1,0)$. What is $T(2,1,0)$?
Original link: http://tinypic.com/r/2mg37dl/5
Hint: Write $(2,1,0)$ as a linear combination of $(1,1,1),(0,-1,2)$ and $(1,0,1)$ and then make use of the fact that $T$ is a linear transformation.