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Finding the transition matrix

  1. May 13, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm enormously frustrated with these problems. I've been trying to figure out how to find out what the transition matrix between C and B is for about 2 hours and I still can't get it. I've watched 4 youtube videos and read two websites as well as the section in my textbook. I still can't get it. Anyway, this one video on youtube said that to get the transition matrix between these two matrices

    [1 -1 0] [-1 1 0]
    [0 0 1] [1 2 1]
    [1 0 2] [0 -1 0]

    you just put them together in a 3 by 6 matrix and reduce it to reduced row echelon form and the 3 by 3 matrix on the right is your transition matrix in this case

    [-2 -5 -2]
    [-1 -6 -2]
    [1 2 1]

    Well that method doesn't work for the problems I'm working on. Number 17 and 21. (I can get 19)

    Screenshot2012-05-13at92646PM.png

    3. The attempt at a solution

    Using this calculator (if I calculated everything by hand I would have wasted 5 hours already)
    http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=roc

    I get

    [5 4 6]
    [4 3 4]
    [-2 -2 3]

    the book says the answer is

    [-7 -6 12]
    [6 5 -10]
    [-4 -4 7]

    I can't get the right answer for 17 either but we'll just worry about 21 for now.
     
  2. jcsd
  3. May 14, 2012 #2
    I'm still open to help for this problem, if anyone is capable.
     
  4. May 16, 2012 #3
    Lets look at problem 21, for instance.
    Observe that:
    [itex]\left(
    \begin{array}{c}
    -1\\
    2\\
    1
    \end{array}
    \right)
    = -7
    \left(
    \begin{array}{c}
    1\\
    0\\
    -1
    \end{array}
    \right)
    + 6
    \left(
    \begin{array}{c}
    1\\
    1\\
    1
    \end{array}
    \right)
    - 4
    \left(
    \begin{array}{c}
    0\\
    1\\
    3
    \end{array}
    \right)
    [/itex]
    So, the first column of my transition matrix will be [itex]
    \left(
    \begin{array}{c}
    -7\\
    6\\
    -4
    \end{array}
    \right)
    [/itex]
    Decomposing the other two B basis vectors in terms of the C basis vectors in similar fashion will yield the two other columns.
     
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