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Matrix inverse problem

  1. Feb 27, 2006 #1
    im doing a matrix inverse problem and have the inverse but when i do the proof the book says it should look like this:

    2 -3 -5/2 -3/2 equals 1 0
    -4 5 times -2 -1 0 1

    but if you muliply those shouldnt you get -10/2 + 6 which doesnt equal 1

    help please
     
  2. jcsd
  3. Feb 27, 2006 #2
    What do you mean by those numbers? Do you mean this:

    [tex]\left(\begin{array}{cc}2&-3\\-4&5\end{array}\right)\times\left(\begin{array}{cc}-5/2&-3/2\\-2&-1\end{array}\right)[/tex]

    If so, that does indeed give you the identity matrix. Check your calculation again.
     
  4. Feb 27, 2006 #3

    VietDao29

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    Homework Helper

    As a matter of fact, it does:
    [tex]\left( \begin{array}{cc} 2 & -3 \\ -4 & 5 \end{array} \right) \times \left( \begin{array}{cc} -\frac{5}{2} & -\frac{3}{2} \\ -2 & -1 \end{array} \right) = \left( \begin{array}{cc} 2 \times \left( -\frac{5}{2} \right) + (-3) \times (-2) & 2 \times \left( -\frac{3}{2} \right) + (-3) \times (-1) \\ -4 \times \left( -\frac{5}{2} \right) + 5 \times (-2) & -4 \times \left( -\frac{3}{2} \right) + 5 \times (-1) \end{array} \right) = \left( \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right)[/tex], the desired result. :)
     
    Last edited: Feb 27, 2006
  5. Feb 27, 2006 #4

    0rthodontist

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    Science Advisor

    -10/2 + 6 = -5 + 6 = 6 - 5 = ?
     
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