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Dividing a row/column of determinant

  1. Apr 11, 2012 #1
    Hi. This is a property but I got confused with it when I thought about the quotient. Look at this:

    [tex]\left| {\begin{array}{*{20}{c}}
    a&d&{2g}\\
    {\frac{1}{3} \cdot 3b}&{\frac{1}{3} \cdot 3e}&{\frac{1}{3} \cdot 6h}\\
    c&f&{2i}
    \end{array}} \right| = \frac{1}{3} \cdot \left| {\begin{array}{*{20}{c}}
    a&d&{2g}\\
    b&e&{2h}\\
    c&f&{2i}
    \end{array}} \right|[/tex]

    I need to transform that matrix into one a b c d e f g h i which I know its determinant is 5. But the teacher instead of taking out the 1/3 she multiplied 3! But doesn't say the property that if you multiply a row then you take out that number and multiply the determinant???
    Thanks!
     
  2. jcsd
  3. Apr 11, 2012 #2

    Dick

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    You can pull the 1/3 out but that doesn't leave the matrix you've shown. What happened to the 3's?
     
  4. Apr 11, 2012 #3
    If I have 6h and I multiply it by 1/3 then I get 2h.
     
  5. Apr 12, 2012 #4

    Dick

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    I don't get it. You can pull the 1/3 out leaving 6h in the matrix, or you can leave it in and have 2h in the matrix. You can't have both.
     
  6. Apr 12, 2012 #5
    Oh yeah, now I realize. It's a colossal stupidity! Sorry for the trouble and thanks!
     
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