How to I find T(0,1,1)?

Question

Let T be a linear transformation from $R^3$ to $R$ such that $T(1,1,1) = 1$, $T(1,1,0) = 2$ and $T(1,0,0) = 3$. Find $T(0,1,1)$. I'm trying to solve it by this way: $R1 - R3$ -> $R1$. Is it correct? $$ \left[ \begin{array}{ccc|c} 1&1&1&1\\ 1&1&0&2\\ 1&0&0&3\\ \end{array} \right] $$ =>$$ \left[ \begin{array}{ccc|c} 0&1&1&-2\\ 1&1&0&2\\ 1&0&0&3\\ \end{array} \right] $$

Answer 1

Since $$ (0,1,1) = (1,1,1) - (1,0,0), $$ we have \begin{align} T(0,1,1) &= T((1,1,1) - (1,0,0))\\ &= T(1,1,1) - T(1,0,0)\\ &= 1 - 3\\ &= -2. \end{align}