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Quick doubt about linear application and its matrix

  1. Jun 7, 2013 #1
    1. The problem statement, all variables and given/known data
    Let ##f:\mathbb{R}^3\to \mathbb{R}^3## such that ##v_1=(1,0,1) , v_2=(0,1,-1), v_3=(0,0,2)## and ##f(v_1)=(3,1,0), f(v_2)=(-1,0,2), f(v_3)=(0,2,0)##
    find ##M^{E,E}_f## where ##E=(e_1,e_2,e_3)## is the canonical basis.


    3. The attempt at a solution
    i see
    ##v_1=e_1+e_3##
    ##v_2=e_2-e_3##
    ##v_3=2e_3##
    thus
    ##f(e_1)+f(e_3)=(3,1,0)##
    ##f(e_2)-f(e_3)=(-1, 0 ,2)##
    ##2f(e_3)=(0,2,0)##
    solving the system i get
    ##f(e_3)=(0,1,0)##
    ##f(e_1)=(3,0,0)##
    ##f(e_2)=(-1,1,2)##

    and so I thought the matrix was:

    (3 -1 0)
    (0 1 1)
    (0 2 0)

    but according to my book the solution should be:
    (3 0 0)
    (-1 1 2)
    (0 1 0)

    why? shouldn't the image of the vector form the columns instead of the rows?
    thank you in advance :)
     
  2. jcsd
  3. Jun 7, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Your answer looks right assuming the vectors are column vectors. Perhaps the book is treating them as row vectors and multiplying the matrix on the right?
     
  4. Jun 7, 2013 #3
    i don't see why it would do that though.
    it's just wrong, probably
    thank you :)
     
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