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I'm having a problem with doing an exercise in construction of a matrix by a given linear transformation. So I understand ex. $f(x,y) = (2x, -y)$ is \begin{matrix} \\ 1 & 0\\ 0 & 1 \\ \end{matrix} transform with this:

\begin{matrix} \\ 2x\\ -y\\ \end{matrix} results this: \begin{matrix} \\ 2 & 0\\ 0 & -1 \\ \end{matrix}

but now I have something like this: "In format $(m,n)$, matrix of linear transformation

1) $h(x) = (5x, x)$ is $(0,1), (1,0), (2,1)$

2) $f(x,y,z) = x + 2y$ is $(2,2),(2,1),(1,3)$

3) $g(x,y,z) = (x,z)$ is $(2,3), (3,2), (2,2)$

4) $s(x,y) = x + y$ is $(2,1), (1,2), (1,1)$

The task is to circle the correct one, how should I go about finding out which one is correct?

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Is this how the question was written? Regards. – Amzoti Jan 7 '13 at 17:57
What's $(m,n)$? – Jack Jan 7 '13 at 20:40
This is exactly what it's written, and this was a question from the last year test. – user55348 Jan 7 '13 at 20:50

The question is asking you for the dimension of the linear transformation.

What is the size of the output vector? That is the first number $m$. How many input variables are there? That is the second number $n$.

For example $h(x)=(5x,x)$ produces a vector of dimension $2$, and takes in a single number $x$. Therefore the dimension of the transformation is $2\times 1$.

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Yeah thanks, I didn't really understood the question, so 1)(2,1) 2)(1,3) 3) (2,3) 4) (1,2) – user55348 Jan 7 '13 at 20:50

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