1. Not finding help here? Sign up for a free 30min 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!

Linear transformations formula

  1. May 14, 2007 #1
    Linear transformations....

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

    Can't figure these things out for my life. Seriously. Here's an example.

    consider the basis S={v1, v2, v3} for R^3 where v1=(1,2,1), v2=(2,9,0) and v3=(3,3,4) and let T:R^3-->R^2 be the linear transformation such that:

    T(v1)=(1,0) T(v2)=(-1,1) T(v3)=(0,1)

    Find formula for T(x1,x2,x3) and use it to find T(7,13,7)

    2. Relevant equations

    3. The attempt at a solution

    So here I am starting it, writing c1(1,2,1)+c2(2,9,0)-C3(3,3,0) to make C1+2C2+3C3, 2C1+9C2+3C3, C1+C3

    c1+ +4c3=x3

    Now, I'm having trouble solving for c1, c2, and c3. The answers seem to be c1=36x1+8x2+21x3, c2=5x1-x2-3x3, c3=9x1-2x2-5x3. I don't know where those numbers came from. (I was guessing putting it into a matrix and use row reduction, but...no). Hmm? Help?
  2. jcsd
  3. May 14, 2007 #2
    So the question is asking for the matrix that sends (1,2,1), ..., to their respective vectors in lR^2.

    A v1 = ?
    A v2 = ?
    A v3 = ?

    It seems like you are trying to find linear combinations of the vectors that will give the transformations. I don't think that is going to work.

    If you can find the matrix that performs the transformations, you can use matrix multiplication to find the vectors corresponding to certain coordinates (c1,c2).
    Last edited: May 14, 2007
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Linear transformations formula
  1. Linear transformation (Replies: 4)

  2. Linear transformation (Replies: 18)