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Math Help - Gauss reduction with constants a and b

  1. #1
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    Gauss reduction with constants a and b

    Consider the system of linear equations:

    x + 2y + 3z = 4
    x + y - 2z = a
    2x + 3y + bz = 6

    where a and b are constants

    For which values of a and b does this system have (i) a unique solution; (ii) no solution; (iii) in finitely many solutions?

    Would you first have to gauss reduce this matrix to get 0s below the first non-zero entry of the first row, second row and third row, and then look at what values of a and b that give the particular solutions? Or would you look for the a and b values that give the particular solutions without gauss reduction?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by SyNtHeSiS View Post
    Consider the system of linear equations:

    x + 2y + 3z = 4
    x + y - 2z = a
    2x + 3y + bz = 6

    where a and b are constants

    For which values of a and b does this system have (i) a unique solution; (ii) no solution; (iii) infinitely many solutions?

    Would you first have to gauss reduce this matrix to get 0s below the first non-zero entry of the first row, second row and third row, and then look at what values of a and b that give the particular solutions? Or would you look for the a and b values that give the particular solutions without gauss reduction?
    If the determinant of the matrix of coefficients is non-zero there is a unique solution. So you could start by looking at the determinant.

    CB
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