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For each of the following linear transformations, write down its matrix and describe the transformation

a) $g(x,y)=(4x,6y)$

b) $h(x,y)=(x+2y,y)$

c) $k(x,y)=(y,x)$

So I have worked out the matrices:

$\begin{bmatrix} 4 & 0 \\ 0 & 6 \end{bmatrix}$

$\begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}$

$\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$

Not sure what the transformations would be?

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    you are correct! – 2017-02-13
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    For example, for the first case the transformation is $$T\binom xy=\begin{pmatrix}4&0\\0&6\end{pmatrix}\binom xy$$ – 2017-02-13
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    Next time use:http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – 2017-02-13

2 Answers 2

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The "describe" part is asking you what each transformation does to the input $(x,y)$; think of this as a vector in $\mathbb{R}^2$. For example, a transformation that sends $(x,y)$ to $(-x,y)$ is a reflection over the $y$-axis.

Start with the transformation $k$; that has a nice "symmetry".

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You would describe g as stretching plane in the x-direction by a factor 4 and in the y-direction by a factor of 6.