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Math Help - Invertible matrices

  1. #1
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    Invertible matrices

    Are there conditions for a Matrice to be invertible or not?

    And why det(A)=0 when A is invertible? Can someone give me a proof? , thank you.
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  2. #2
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    Re: Invertible matrices

    I think I found the answer, I am not sure though, so if Matrix A is invertible then rankA=n when n is the number of columns or unknowns. However if RankA<n then we have a row with just only 0 and according to the properties of Determinants if we have a row with only zeros then detA=0

    Is this correct?
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  3. #3
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    Re: Invertible matrices

    Quote Originally Posted by davidciprut View Post
    Are there conditions for a Matrice to be invertible or not?

    And why det(A)=0 when A is invertible? Can someone give me a proof? , thank you.
    if det(A)=0, A is not invertible. There are a bunch of equivalent conditions for whether an nxn matrix is invertible. Basically it must have n linearly independent columns.
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