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Linear algebra, linear trasformation

  1. Mar 17, 2013 #1
    1. The problem statement, all variables and given/known data

    let b1=(1,1,0)T ;b2=(1 0 1)T; b3=(0 1 1)T

    and let L be the linear transformation from R2

    into R3 defined by

    L(x)=x1b1+x2b2+(x1+x2)b3

    Find the matrix A representing L with respect to the bases (e1,e2)
    and (b1,b2,b3)

    2. Relevant equations



    3. The attempt at a solution

    First thing I did was label out my e1 and e2

    e1=(1,0)

    e2=(0,1)

    L(e1)=b1+b3
    = (1,2,1)T

    L(e2)=b2+b3
    =(1,1,1)T

    So I would assume my A to be (L(e1),L(e2))T
    However that is incorrect.

    I'm not sure what I am doing incorrect the book does the same steps, but gets a different answer.
     
    Last edited by a moderator: Mar 17, 2013
  2. jcsd
  3. Mar 17, 2013 #2

    Fredrik

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    Staff Emeritus
    Science Advisor
    Gold Member

    Row i, column j of A is ##(Le_j)_i## (i.e. the ith component of ##Le_j## in the given ordered basis). This makes ##Le_1## the first column, but you made it the first row.

    Also, you computed ##b_2+b_3## wrong.
     
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