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Stuck finding a specific value of an inverse of a complex matrix

  1. Nov 3, 2016 #1
    1. The problem statement, all variables and given/known data
    Consider the following matrix.

    A =

    2 + 4i.........1 + 5i

    2 − 3i.........2 + 3i

    Let B = A-1. Find b12 (i.e., find the entry in row 1, column 2 of A−1)

    2. Relevant equations

    A-1 = 1/(ad - cb)*
    [ d -b ]
    [ -c a ]
    <--imagine as 2x2 matrix with first row (d,-b) and second row (-c,a)

    3. The attempt at a solution

    1/(ad - cb) =

    1/((2+4i)(2+3i) - (2-3i)(1+5i))

    1/((4+14i-12) - (2+7i+15))

    1/(4+14i-12-2-7i-15)

    1/(-25+7i)

    [(d,-b)(-c,a)] =

    [ d -b ]
    [ -c a ] =

    2 + 3i.........-1 - 5i

    -2 + 3i.........2 + 4i

    So for first row, second column, we should be multiplying 1/(-25+7i) by -1 - 5i. I'm getting -10/576 + 12i/576, but my answer is wrong. Where is my mistake?
     
  2. jcsd
  3. Nov 3, 2016 #2
    I just realized my mistake, it was arithmetic.
     
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