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Math Help - finding general algorithm

  1. #1
    jumpingpanda
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    finding general algorithm

    it says that i need to find a general algorithm for solving determinants if matrices using minors of the first row for matrices larger than 2x2.

    I also need to do the same thing for solving a system of n linear quations with n independent variables using determinants.

    I know how to solve for both... but i'm having trouble writing a gereal algorithm for it.

    thank you sooo much
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  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    Quote Originally Posted by jumpingpanda View Post
    it says that i need to find a general algorithm for solving determinants if matrices using minors of the first row for matrices larger than 2x2.

    I also need to do the same thing for solving a system of n linear quations with n independent variables using determinants.

    I know how to solve for both... but i'm having trouble writing a gereal algorithm for it.

    thank you sooo much

    i'll put the first one this way:

    Let A be the nxn matrix.
    represent the Minor of the first row by det (M_{1,j}) = |M_{1,j}| where M_{1,j} is the (n-1)x(n-1) matrix obtained by deleting the first row and the jth column, j runs from 1 to n.

    det A = a_{1,1}(-1)^{1+1}|M_{1,1}| + a_{1,2}(-1)^{1+2}|M_{1,2}| + ... + a_{1,n}(-1)^{1+n}|M_{1,n}| = \displaystyle\sum_{j=1}^n a_{1,j}(-1)^{1+j}|M_{1,j}|
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