1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Linear transformations

  1. Apr 20, 2008 #1
    [SOLVED] Linear transformations

    1. The problem statement, all variables and given/known data

    Determine whether the following maps are linear transformations. (proofs or counterexamples required)

    a.) L: R^2[tex]\rightarrow[/tex]R^2,

    (2x1 + 3x2)

    The brackets should be two large brackets surrounding the two vectors.

    3. The attempt at a solution
    I've been reading about linear transformations and i know i have to show something like:

    L(x1+x2)= L(x1) +L(x2) and L(cx1)= cL(x1) where c is a scalar.

    Is this right and i should treat x1 and x2 separately rather than the vector including x1 and x2 as one element of R^2?

    What im trying to say is, do i need to define a vector (y1, y2) aswell in the set of R^2?
    Last edited: Apr 20, 2008
  2. jcsd
  3. Apr 20, 2008 #2
    For x,y [tex]\in[/tex]R^2,

    x=(x1,x2) and y= (y1,y2)

    x+y=(x1,x2)+(y1,y2)= (x1+y1, x2+y2)
    L(x+y) = L(x1+y1, x2+y2)
    =L(x) +L(y)

    Is this right for the first part?

    Then because cx= c(x1,x2) = (cx1,cx2) you have
    L(cx) = L(cx1, cx2) = (2cx1 + 3cx2)
    =c(2x1 + 3x2)

    I think i'm understanding it more now, if this is right that is.
  4. Apr 20, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    That's right. I think you've got it.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook