A linear transformation is given: $\displaystyle T:R^3 -> R^3$ such as:

$\displaystyle T(1,1,1)=(1,1,1)$

$\displaystyle T(0,1,0)=(0,1,0)$

$\displaystyle T(1,0,2)=(1,0,1)$

Find $\displaystyle T(x,y,z)$ and $\displaystyle [T]_E$ $\displaystyle (E={(1,0,0),(0,1,0),(0,0,1)})$

I know that first you must prove that (1,1,1),(0,1,0) and(1,0,2) are linearly independent which is not a problem my problem is finding $\displaystyle T(x,y,z)$

Thanks in advance.