# How to I find T(0,1,1)? [closed]

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? $$\left[ \begin{array}{ccc|c} 1&1&1&1\\ 1&1&0&2\\ 1&0&0&3\\ \end{array} \right]$$ =>$$\left[ \begin{array}{ccc|c} 0&1&1&-2\\ 1&1&0&2\\ 1&0&0&3\\ \end{array} \right]$$

## closed as off-topic by user223391, Did, Dando18, user284331, Trevor GunnMay 9 '18 at 3:53

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• $T$ is linear. What does that mean to you? – Arthur May 8 '18 at 14:19
• Use matrix to solve? – Vinh Quang Tran May 8 '18 at 14:23
• What is your try. Please add you try to the question. – Amin235 May 8 '18 at 14:26
• Matrices are part of the theory around linear transformations, yes. And this can probably be solved with matrices. But that's not what I asked you about. I did not ask what consequences "$T$ is linear" has on how one would solve the problem. That is the next step. I asked what you think "linear transformation" means. Without that you can't even begin to solve this problem. – Arthur May 8 '18 at 14:28
• I added my try to the question. – Vinh Quang Tran May 8 '18 at 14:31

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}
• This is wrong. You need to take another look at $-T(1,0,0)$. – Arthur May 8 '18 at 14:50