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Show that a reflection of each vector $\vec{x}=(x_1, x_2, x_3)$ through $x_3=0$ onto $T(\vec{x})=(x_1, x_2, -x_3)$ is linear.

I think it somehow involves the Transformation Matrix: $A=\begin{bmatrix}1&0&0 \\ 0&1&0 \\ 0&0&-1\end{bmatrix} \times \vec{x}$, resulting in $(x_1, x_2, -x_3)$ but i'm not sure. I'm wondering if it has something to do with the superposition principle but i'm also not sure.

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    LaTeX is a nice touch, but don't let it stop you from doing anything. If you're looking for a crash course we have [this](http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference). Most of what you've written is already in proper form. All you have to do is wrap it in dollar signs.2012-09-11
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    You need to show that (i) $T(\vec{x}+\vec{y}) = T(\vec{x})+T(\vec{y})$, and (ii) $T(\lambda \vec{x}) = \lambda T(\vec{x})$.2012-09-11
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    @axblount ah i see, i was trying the $ in the beginning but missed that i had to have one at the end so I just got rid of it.2012-09-11

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