A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

sh3lsh

  • one year ago

Linear Transformation Question

  • This Question is Closed
  1. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Describe all linear transformations from \[\mathbb{R}^{2}\] to \[\mathbb{R}\]. What do their graphs look like?

  2. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Also, how do I clean up this latex? As in, how do I make sure it doesn't make space?

  3. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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)

  4. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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 ?

  5. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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 \(\mathbb{R}\)

  6. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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....

  7. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    gtg gb

  8. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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!

  9. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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!)

  10. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    f(x,y) = x^2+y^2 represents a "surface" in 3D |dw:1436716545738:dw|

  11. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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)

  12. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.