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Math Help - -proof help for upcoming exam-eigenvalue

  1. #1
    n22
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    -proof help for upcoming exam-eigenvalue

    Hello,
    I dont think I've posted this one before....
    Prove that Null(A)={0} iff λ=0 is not an eigenvalue of A.How do i answer this question ?
    And ..i dont really know how to write math proofs well..is there a general structure that I can memorise so that I may apply it when neccessary to many other proofs for linear algebra.?
    thanks.
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  2. #2
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    Re: -proof help for upcoming exam-eigenvalue

    Hi, I would say that Null(A)= \{0\} iff A as a square matrix is regular (because of uniqueness of the solution of system Ax=b for any b)
    on the other hand \lambda=0 is an eigenvalue of the square matrix A iff A is singular

    can you use that?
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  3. #3
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    Re: -proof help for upcoming exam-eigenvalue

    What does "0 is an eigenvalue of A" mean? Your result is a direct consequence of the definition.
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