# 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.

https://brainmass.com/math/basic-algebra/basis-eigenspace-43659

#### Solution Summary

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

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