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Let $T : \mathbb{R}^2 -> \mathbb{R}^3$ be a linear transform such that $$T(\begin{bmatrix} 1\\ 1 \end{bmatrix} ) = \begin{bmatrix} 2\\ 1\\ 1 \end{bmatrix} $$ and $$T(\begin{bmatrix} 1\\ 2 \end{bmatrix} ) = \begin{bmatrix} 1\\ 3\\ 1 \end{bmatrix} $$

Find $$T( \begin{bmatrix} 1\\ 0 \end{bmatrix} ) $$

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Hint: Note that $$ \pmatrix{1\\0} = 2 \pmatrix{1\\1} - \pmatrix{1\\2} $$

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    I got a 3x1 matrix with elements {3, -1, 1}. Is this correct? – 2017-02-04
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    That's correct. – 2017-02-05