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Math Help - [SOLVED] Find nullspace given eigenvalues

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    [SOLVED] Find nullspace given eigenvalues

    Hi,
    Suppose A has eigenvalues 0,3,5 with independent eigenvectors u,v,w.
    Give a basis for the nullspace and a basis for the column space.
    Could you please explain this to me?
    Thanks
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    Hello,
    Quote Originally Posted by tbyou87 View Post
    Hi,
    Suppose A has eigenvalues 0,3,5 with independent eigenvectors u,v,w.
    Give a basis for the nullspace and a basis for the column space.
    Could you please explain this to me?
    Thanks
    The nullspace maps to the zero element.

    Since A has an eigenvalue 0 with associated eigenvector u, we have :
    A \bold{u}=0 \bold{u}=0
    So u belongs to the nullspace, along with the null vector which always belongs to the nullspace.

    The other ones form a basis for the column space.
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