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Math Help - Proof help (related to characteristic polynomials and Cayley-Hamilton)

  1. #1
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    Proof help (related to characteristic polynomials and Cayley-Hamilton)

    I'm a bit stuck on where to start on this proof. The problem reads:

    "Let A be an n x n matrix with characteristic polynomial:

    f(t) = (-1)^nt^n + a(n-1)t^{n-1} + ... + a(1)t + a(0)

    Prove that A is invertible iff a(0) is not equal to Zero.

    The (n-1), (1) and (0) are subscripts, my apologies I don't have/know how to use Latex to form the equations appropriately.
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  2. #2
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    Quote Originally Posted by flabbergastedman View Post
    I'm a bit stuck on where to start on this proof. The problem reads:

    "Let A be an n x n matrix with characteristic polynomial:

    f(t) = (-1)^nt^n + a(n-1)t^{n-1} + ... + a(1)t + a(0)

    Prove that A is invertible iff a(0) is not equal to Zero.

    The (n-1), (1) and (0) are subscripts, my apologies I don't have/know how to use Latex to form the equations appropriately.

    Well, just prove that a_0=(-1)^ndet(A)

    Tonio
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  3. #3
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    ugh I must have been falling asleep when I was looking at this problem. I just remembered that fact, especially given that a_o is not equal to 0. Thank you!
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