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Homework Help: Finding Matrix B from given info

  1. Feb 9, 2017 #1
    1. The problem statement, all variables and given/known data
    Use the given info to find matrix B

    2. Relevant equations
    (I + 3B)^-1 = [5 2; 4 2]

    to make more clear:

    inv(I + 3B) = this 2x2 matrix: top row = 5 2, bottom row = 4 2

    3. The attempt at a solution
    I tried multiplying both sides of the eqn by I + 3B to get I = [5 2; 4 2](I + 3B)
    Then tried to multiply the two quantities (using B = [a b; c d])
    Tried to set that product equal to the identity matrix and solve for the unspecified constants, a b c d.
    After that I plugged the values into the the product found in the previous step
    I then should have acquired the correct matrix B, but alas, it wasn't even close.
    If I am overlooking some elementary matrix 'algebra', or any hints at all would be greatly appreciated.
    Thank you!
  2. jcsd
  3. Feb 9, 2017 #2
    Why not just calculate the matrix inverse of the 2x2 matrix on the RHS?
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