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    Find a basis for an eigenspace without computing the characteristic polynomial.

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    Without computing the characteristic polynomial, explain why the matrix A below has 0 as eigenvalue; then find a basis for the corresponding eigenspace.

    A =

    1 -1 1
    -1 1 -1
    1 -1 1.

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    Solution Summary

    A basis for an eigenspace is found without computing the characteristic polynomial. The solution is detailed and well presented.