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I get question from my teacher. he ask what this matrix transformation do:

options:

1) rotate and scaling

2) translate and scaling

3) scaling and rotate

4) not 1,2,3

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

we working on 2D with homegeneous cordinates.

thank you

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    Are we supposed to think of this as a transformation on $2$-dimensional space or on $3$-dimensional space? – 2017-02-16
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    Do you know the basic forms of rotations, scalings, and translations? Are you using homogeneous coordinates for two dimensions (like in graphics) or are you dealing in three dimensions? – 2017-02-16
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    @Omnomnomnom we work on 2D with homogenous cordination – 2017-02-16
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    Now that we're on the same page, then: what have you tried? Do you have any "guesses" here? Any ideas? – 2017-02-16
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    I don't know how to solve it, if you can to explain please. – 2017-02-16
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    What do you know about rotations, scaling, and translations? Please give some context about what you know so that others know that you've thought about the problem. Otherwise, such a question is likely to be downvoted and closed. – 2017-02-16
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    I learn in computer graphics course about the affine transformations. scalling - increse/decrease the object. rotate - rotate the object by specific angle. translate - move the object. but it's very strange for me that all the Y coordinate will go to 0, so I can't to recognize what this matrix do. – 2017-02-16
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    There is no "scaling" going on here, so the answer has to be 4). – 2017-02-16
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    @Omnomnomnom , my teacher said that because all Y cordinates go to 0 after the transformation so it's scalling, he wrong, right? – 2017-02-16
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    @user2540615 you already had an answer to this question from the teacher. This is the kind of context that should be included with your question. – 2017-02-16
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    @Omnomnomnom I'm not write it because I really think it wrong, that why I ask here. thank you – 2017-02-16
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    @user2540615 in any case, it could be that "scaling" means something else in the computer-science world. In math, scaling usually means that we multiply all coordinates by the same value. For example, $$ (x_1,x_2,x_3) \mapsto (10 x_1,10x_2,10x_3\) $$ would be a scaling, but $$ (x_1,x_2,x_3) \mapsto (10 x_1,100x_2,1000x_3\) $$ would not. The matrix in your question is this "second kind of scaling", where we multiply coordinates by distinct values. – 2017-02-16
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    @Omnomnomnom so if we suppose that in computer-science scalling it's not uniform, so it's possible to multiply by 0 and call it scalling? thank you very very much – 2017-02-16
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    @user2540615 yes, that's what I think – 2017-02-16
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    @user2540615 Even if you thought his answer was wrong, you should have still said something about it. That gives us some important information about why you're asking us this question in the first place. Also, it lets us know that you have put some effort into answering your own question. – 2017-02-16

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This matrix denotes a "scaling and translation" in the sense that $$ \pmatrix{1&0&1\\0&0&1\\0&0&1}\pmatrix{x\\y\\1} = \pmatrix{1 \cdot x+1\\0 \cdot y+1\\1} $$ which is to say that our new coordinates are $(1 \cdot x,0 \cdot y) + (1,1)$