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Trouble solving this Determinant

  1. Oct 8, 2009 #1
    I'm having trouble solving this question:

    If det

    | a b c |
    | p q r | = 2,
    | u v w |

    find det (3B^-1) where B =

    | 2u 3u-a a-p |
    | 2v 3v-b b-q |
    | 2w 3w-c c-r |

    Is it possible to transpose B?

    So far what I got is 4; however, the instructor told me that the answer is |B| = 27/4
     
  2. jcsd
  3. Oct 8, 2009 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Re: Determinants

    Remember there is a difference between a determinant and a matrix. I'm guessing you are given a matrix

    [tex]B =\left [
    \begin{array}{ccc}
    2u&3u-a&a-p\\
    2v&3v-b&b-q\\
    2w&3w-c&c-r

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

    and what you have written is its determinant. Remember when you multiply a matrix by 3 it multiplies every element in the matrix. So for an n by n matrix A, if you multiply it by 3 and take its determinant, a 3 comes out of every column so

    det(3A) = 3ndet(A)

    That plus the fact that det(A-1) = 1 / det(A)
    should help you out.
     
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