sh3lsh
  • sh3lsh
Linear Transformation Question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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sh3lsh
  • sh3lsh
Describe all linear transformations from \[\mathbb{R}^{2}\] to \[\mathbb{R}\]. What do their graphs look like?
sh3lsh
  • sh3lsh
Also, how do I clean up this latex? As in, how do I make sure it doesn't make space?
sh3lsh
  • sh3lsh
http://www.math.utah.edu/~richins/teaching/2270/test1solns.pdf 4 is the solution, but why is A is the 1x2 matrix? I was under the impression because you're going from R^2 to R, from two dimensions to one dimension, the surface would become a line. (a plane to a line)

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ganeshie8
  • ganeshie8
Let me ask you a side question : How does the graph of a function from R^2 to R like : \(f(x,y) = x^2 + y^2\) look like ?
SolomonZelman
  • SolomonZelman
The latex advise... b/c igtg soon. if you type `\(\mathbb{R}^{2}\)` then you get \(\mathbb{R}^{2}\) if you type `\(\mathbb{R}\)` then you get \(\mathbb{R}\)
SolomonZelman
  • SolomonZelman
In general if you type something in equation editor, and then after entering the equation(s) entirely, you can change `\[ \]` to `\( \)` and that will allow you to write on the same line with latex. Sometimes you will need to add a `\displaystyle` or such....
SolomonZelman
  • SolomonZelman
gtg gb
sh3lsh
  • sh3lsh
If I view \(f(x,y)=x^2 + y^2 \) (thanks @SolomonZelman !) in a two dimensional manner, I would see small planes, so in the same vein, the answer would obviously be that I would view planes!
sh3lsh
  • sh3lsh
Let me understand some theory of Calc III again. If f(x,y) is free to choose whatever value it wants, doesn't it really constitute as another variable? So that, z = x^2 + y^2 is identical to f(x,y) = x^2 + y^2? Am I misunderstanding this? Thinking of it as another variable, I think of it being a three-D object going down to a two-D object, so the object would have to be a plane. I don't understand how this could relate back to linear transformations. (if you think this is completely wrong to the point it's unexplainable to me, tell me! I'll pursue help in our math lab when it opens!)
ganeshie8
  • ganeshie8
f(x,y) = x^2+y^2 represents a "surface" in 3D |dw:1436716545738:dw|
ganeshie8
  • ganeshie8
Since the domain is 2D and image is 1D, the graph is a surface in 3D (the function maps each point in xy plane to a real number)

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