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Math Help - Determinant

  1. #1
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    Determinant

    Let A be a 3x3 matrix which satifies the equation:

    A^3 -3A^2 - 10A = 0

    a) Find all the real numbers which could possibly be eigenvalues of A

    alright... so what i did was simplify the equation and got (A)(A-5)(A+2)=0

    but I don't know where to go from there

    and

    b) Assume, in addition that detA = 20. Find det(A^2 -3A)

    I know what to do if i had the matrix but i dont so im kinda lost on this one

    thanks
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  2. #2
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    Quote Originally Posted by treetheta View Post
    Let A be a 3x3 matrix which satifies the equation:

    A^3 -3A^2 - 10A = 0

    a) Find all the real numbers which could possibly be eigenvalues of A

    alright... so what i did was simplify the equation and got (A)(A-5)(A+2)=0

    but I don't know where to go from there

    and

    b) Assume, in addition that detA = 20. Find det(A^2 -3A)

    I know what to do if i had the matrix but i dont so im kinda lost on this one

    thanks
    a) Therefore \lambda = 0, 5, -2 since a matrix satisfies its characteristic equation (Cayley-Hamilton theorem).

    b) Left multiply A^3 -3A^2 - 10A = 0 by A^{-1} and simplify: A^2 - 3A = 10 I. Therefore ....
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  3. #3
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    the determinant is equal to 1000

    10(10-0) = 100

    wow, your so smart =D but how would i ever think of that thanks, for the tip though it will help me look out for tricks
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