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 transformation matrix

  1. Jul 4, 2010 #1
    1. The problem statement, all variables and given/known data

    Let L: R^3 -> R^3 be a linear transformation such that

    L(i) = [1 2 -1], L(j) = [1 0 2] and L(k) = [1 1 3].

    Find L([ 2 -1 3)].

    All the numbers in [ ] should be vertical, but I don't know how to set that up.

    2. Relevant equations

    3. The attempt at a solution

    I'm not sure how to even approach this. I've tried looking at examples in the text and they aren't clear.

    I would think that you make a matrix L with the three columns i j k as above. and x = [2 -1 3] and just calculate Lx=b to find b.

    But a similar problem in the text has a single number answer. I would've guessed that it gives a vector.
  2. jcsd
  3. Jul 4, 2010 #2


    User Avatar
    Homework Helper

    You know how the transformation acts on the basis {i, j, k}. Let v be any vector, then v = αi + βj + γk. Then L(v) = αL(i) + βL(j) + γL(k).

    The vectors L(i), L(j) and L(k) are the columns of the matrix representation of the operator L.
  4. Jul 4, 2010 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You should get a vector here. Maybe you should post the similar problem and we can help you figure out what the difference is?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook