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Linear Algebra Find the Standard Matrix of T

  1. Feb 2, 2013 #1
    1. The problem statement, all variables and given/known data

    Let T be a linear transformation from R3 to R3. Suppose T transforms (1,1,0) ,(1,0,1) and (0,1,1) to (1,1,1) (0,1,3) and (3,4,0) respectively.

    Find the standard matrix of T and determine whether T is one to one and if T is onto
     
  2. jcsd
  3. Feb 2, 2013 #2

    tiny-tim

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    welcome to pf!

    hi x.x586! welcome to pf! :wink:

    show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
     
  4. Feb 2, 2013 #3
    I know T(x) =Ax=[T(e1) ,T(e2,) T(e3)]

    I thought A would just be the matrix with columns (1,1,1) (0,1,3) and (3,4,0), but then I realized that
    (1,1,0) ,(1,0,1) and (0,1,1) are not the standard basis vectors for R3


    My book doesn't give any examples where we don't start with the standard basis vectors

    Should I have started by taking a 3x3 matrix entries [x1,x2,x3;x4,x5,x6,x7,x8,x9] and multiply that by a 3x3 matrix with entries [1,1,0;1,0,1;0,1,1] and set that equal to a matrix with entries [1,0,3;1,1,4;1,3,0] and then got a system of equations from there by multiplying the left side out. And then set up an augmented matrix and used row reduction to find corresponding entries for A?
     
    Last edited: Feb 2, 2013
  5. Feb 2, 2013 #4

    tiny-tim

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    hi x.x586! :smile:

    (i'm not guaranteeing this is the quickest way, but …)

    if you can express eg (1,0,0) as a(1,1,0) + b(1,0,1) + c(0,1,1), then you'll have the form you're familiar with :wink:
     
  6. Feb 2, 2013 #5
    Thank you.
     
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