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Finding the inverse and finding a matrix * A = 0 matrix

  1. Sep 29, 2005 #1
    Hello everyone!! Matrices fun! Anyways,
    I'm trying to find a matrix that is equal to the idenity matrix if u multiply 2 matrices together. Well that matrix is the inverse So i'm trying to find the inverse but the answer is wrong:
    A =
    -5 3
    2 -9

    So i found the determinant and i switched the a and d, and negated the c and b . isn't htat the inverse?

    1/35-6 = 1/29


    -9 -3
    -2 -5

    -9/29 -3/29
    -2/29 -5/29

    isn't thtat the inverse of A?

    I also have B =
    -1 6
    5 -30

    I need to multiply that by some matrix C so the resultant matrix is
    0 0
    0 0
    but i can't just say C is equal to
    0 0
    0 0
    any ideas? thanjks!

    I did notice, Row 1 is just 1/5 row 2
     
  2. jcsd
  3. Sep 29, 2005 #2

    TD

    User Avatar
    Homework Helper

    You have to switch a and d, also switch b and c and then change the signs of these last 2. After that, you have to divide by the determinant. So:

    [tex]A = \left( {\begin{array}{*{20}c}
    a & b \\
    c & d \\

    \end{array} } \right) \Rightarrow A^{ - 1} = \frac{1}
    {{\det A}}\operatorname{adj} A = \frac{1}
    {{ad - bc}}\left( {\begin{array}{*{20}c}
    d & { - c} \\
    { - b} & a \\

    \end{array} } \right)[/tex]

    If you don't "see" it right away, work out the following matrix product to get a system of lineair equations.

    [tex]\left( {\begin{array}{*{20}c}
    { - 1} & 6 \\
    5 & { - 30} \\

    \end{array} } \right) \cdot \left( {\begin{array}{*{20}c}
    a & b \\
    c & d \\

    \end{array} } \right) = \left( {\begin{array}{*{20}c}
    0 & 0 \\
    0 & 0 \\

    \end{array} } \right)[/tex]
     
  4. Sep 29, 2005 #3

    Hurkyl

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    Staff Emeritus
    Science Advisor
    Gold Member

    Multiplying a matrix by something to get zero strongly reminds me of the notion of a null space...
     
  5. Sep 29, 2005 #4
    Thanks TD, but for some reason its still wrong, i got:
    -9/29 -2/29
    -3/29 -5/29
     
  6. Sep 29, 2005 #5

    TD

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    Homework Helper

    Check your determinant again, that is ad-bc :smile:
     
  7. Sep 29, 2005 #6
    lol what the f, (-5)(-9) - (3)(2)
    1/45-6
    1/39 right?
     
  8. Sep 29, 2005 #7

    TD

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    Homework Helper

    Well, the determinant is 39 (so not 29). Then, you have to divide by it indeed.
    So 1/39 * adj(A)
     
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