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Homework Help: Base vectors and matrix

  1. Dec 27, 2006 #1
    1. The problem statement, all variables and given/known data

    The problem is quite easy, but I've still trouble solving this.

    Given the two base vectors e1=(1,-2,0) and e2=(0,3,0) and the other ones of a different vector space w1=(1,0,0) and w2=(0,1,0).

    I've to find a matrix A that that does the following Ae1=w1 and Ae2=w2

    2. The attempt at a solution

    Easy isn't it? I've done what the professor did to solve such problems:

    Calculate: e1=1*w1+(-2)*w2
    and: e2=0*w1+3*w2

    thus that shouls yield the matrix A:(1, 0, 0; -2, 3, 0; 0, 0, 0)
    where ; is written for different lines in the matrix A.

    But if I calculate A*e1 I get something totally wrong.

    Where's the mistake in my calculation?
     
  2. jcsd
  3. Dec 27, 2006 #2
    You calculated the inverse of A, expressing the e vectors as a linear combination of the w vectors:

    Ae1=w1 so e1=A^(-1)w1
    Ae2=w2 so e2=A^(-1)w2

    Clearly, your answer for A is incorrect since the inverse of your A does NOT exist. For this reason, you need to drop the third dimension. So , for example, e1 becomes (1,-2) etc.

    The way you proceed is correct though, except that your A is actually the inverse of A, and the inverse of A is indeed (1,0;-2,3). So acquire A now.

    marlon
     
    Last edited: Dec 27, 2006
  4. Dec 27, 2006 #3
    I don't understand exactly why I've to build the inverse of A, because I search A such that A*e1=w1 not that A*w1=e1.
     
  5. Dec 27, 2006 #4
    ahh, k, I got it know, I took your hint marlon, thanks, thanks.
     
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