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!

Find the linear transformation matrix

  1. Oct 6, 2011 #1
    1. The problem statement, all variables and given/known data
    Suppose that a linear transformation maps a point (2,3) to (0,1) and maps a point (9,7) to (1,0). Find the matrix for this linear transformation.

    2. Solution (answersheet)
    Observe that the two point that are the result of the mapping are the two base vectors.
    If our information would be that (0,1) were mapped to (2,3) and that (1,0) were mapped to (9,7), then the matrix would be easy to write down.
    |9, 2|
    |7, 3|
    But we are in the opposite direction! so the answer is the inverted matrix.

    3. My question
    How would this question be solved if the points wouldn't map to the base vectors? I.o.w. what are the common steps to solve this, that are skipped here? If possible. The only way I know is with homogeneous coordinates, but I couldn't get it to work with this exercise.
     
    Last edited: Oct 7, 2011
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted