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Reversing the Determinant

  1. Oct 12, 2008 #1
    Let there be a 2-by-2 matrix A with the elements:

    [a b]
    [c d]

    Now, let there be a 2-by-2 matrix B with the elements:

    [w x]
    [y z]

    Let A*A = B.

    This means that w, x, y, and z can all be independantly represented solely in terms of a, b, c, and d.

    My question: is there any way for a, b, c, and d to be represented solely in terms of w, x, y, and z?
     
  2. jcsd
  3. Oct 12, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Well, multiplying A*A out, you have a2+ bc= w, ab+ bd= x, ac+ cd= y, and bc+ d2= z. Now it is a matter of solving those 4 equations for a, b, c, and d.
    Those are quadratic equations so there will be more than one solution - as you might expect from the fact that A*A= B is really "quadratic" itself.

    Now, my question is, What does this have to do with the "determinant"?
     
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