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Matrix Question

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  • 11-09-2004 10:27pm
    #1
    Nietzschean
    Registered Users Posts: 7,314 ✭✭✭


    Looking at a question here to do with Jordan matrices, but really thing i'm wondering at the moment....

    I'm trying to get a vector B such that (A-2I)B = 0
    where A = 3 1 -3
    -7 -2 9
    -2 -1 4

    I was attempting to use row reduction to get the kernel, as this would be how i would usually differenciate between
    J = 1 0 0
    0 2 0
    0 1 2
    and
    J = 1 0 0
    0 2 0
    0 0 2

    in solving for PAP^-1 = J

    usuall method would be if dim Ker(A-2I) = 1 then it had to be of the first form there, and if 2 then the second form.


    But alas row reduction only turned up the trivial vector 0,0,0

    i know the vector 1 , -4 , -1 will do it (applied ker(A-2I)^2 to A-2I) ....

    also of note is that the determinant of A-2I = 0 i suppose.


    any idea's on another handy way of getting dim Ker (A-2I) ?


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