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Techniques for solving type of Matrix problems

  1. Sep 29, 2005 #1
    1)
    a)
    If A =
    1 2
    0 3
    and B is an upper-triangular matrix such that tr(B) = 0 and
    AB =
    1 -1
    0 -3
    then B = _____

    AND
    b)
    If A =
    1 5
    -1 3
    and A = B+C where B is symmetric and C is skew-symmetric, then
    B = ___ and C = ____.

    2)
    a)
    If A, B and C are matrices such that A^TB^(-1)C is a column matrix, and A is a 2x5 matrix, then the size of B is _____ and the size of C is ___.

    b)
    If B^(−1)A^TBC is a 6 × 7 matrix, then the size of A is ,
    the size of B is ___, and the size of C is ____.


    Are there some easy techniques that can be used to find the sizes of each of the matrix, such as 2a and 2b? I kind of have an idea of how to do those mentioned in 1a but 1b having a bit trouble. These are not homework questions but questions from old exams. I have an exam coming up and I'm trying to review. Any suggestions would be much appreciated. Thank you
     
  2. jcsd
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