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Math Help - Determinant problem

  1. #1
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    Determinant problem

    A = [ a b . . . b ]
    [ b b . . . b ]
    [ b b . . . a ]

    What is the determinant of A?
    What conditions would allow det A not equal to 0?

    My answers:

    det A = 2a (ba - b^2) or 0, since the middle terms would all be eliminated.

    det A not equal to 0 when a not equal to 0, with the number of row + number of columns = even.
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    A = [ a b . . . b ]
    [ b b . . . b ]
    [ b b . . . a ]

    What is the determinant of A? Mr F says: Are you suggesting that the order of the matrix is 3xm where m > 3. If so, the determinant does not exist.

    What conditions would allow det A not equal to 0?

    My answers:

    det A = 2a (ba - b^2) or 0, since the middle terms would all be eliminated.

    det A not equal to 0 when a not equal to 0, with the number of row + number of columns = even.
    Or do you mean  A = \left( \begin{array}{ccc}<br />
a & b & b \\<br />
b & b & b \\<br />
b & b & a \\ \end{array} \right) \, ? In which case, \det(A) = b(a - b)^2 = 0 when a = b or b = 0.
    Last edited by mr fantastic; January 13th 2008 at 05:16 PM.
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