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Math Help - Matrix

  1. #1
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    Matrix

    I have a revision question in my book about matrices but because I learnt it a year ago I can't quite remember all the details so i'll write what I know and hopefully some of you can help me

    I have a matrix which is (a,b ; c,d) as in ab on top and cd below and I need to find the conditions on abcd so that it is row equivalent to the identity

    For one I know the identity is (1,0 ; 0,1) and im pretty sure the determinant can't be zero in order for it to be row equivalent and equal to the identity but apart from that I don't know the other conditions for it..


    The second question is just to check my answer

    I have (lamda - 2)x + y = 0

    x + (lamda - 2)y = 0

    and I have to find the non trivial solutions

    In order to do this I find the determinant ( lamda squared + - 4 lamda + 4) then make that equal to zero find the solution for lamda then the non trival solutions are all those except where lamda makes the determinant zero? is that correct?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by CookieC View Post
    For one I know the identity is (1,0 ; 0,1) and im pretty sure the determinant can't be zero in order for it to be row equivalent and equal to the identity but apart from that I don't know the other conditions for it..


    The condition \det A\neq 0 is necessary and sufficient.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by CookieC View Post
    I have (lamda - 2)x + y = 0

    x + (lamda - 2)y = 0

    and I have to find the non trivial solutions

    In order to do this I find the determinant ( lamda squared + - 4 lamda + 4) then make that equal to zero find the solution for lamda then the non trival solutions are all those except where lamda makes the determinant zero? is that correct?

    \det A=(\lambda-2)^2-1=0\Leftrightarrow \lambda=3\;\vee\;\lambda=1

    If \lambda \neq 3\;\wedge\; \lambda \neq 1 there are no trivial solutions. For \lambda =3\;\vee\; \lambda \neq 1 the system has more than one solution so, it has non trivial solutions.
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