The eigenvectors of a square matrix A are all non-zero vectors v such that Av= lambda v for some scalar lambda , called the eigenvalue For example if A=([5,1,-1],[4,2,-4],[3,-3,1]) then we can directly calculate that ([5,1,-1],[4,2,-4],[3,-3,1])([1],[0],[1])= 9. ([5,1,-1],[4,2,-4],[3,-3,1])([1],[0],[1])= a So we have demonstrated that ([1]

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The eigenvectors of a square matrix A are all  non-zero vectors v such that Av= lambda v for some scalar  lambda , called the eigenvalue For example if A=([5,1,-1],[4,2,-4],[3,-3,1]) then we can directly calculate that ([5,1,-1],[4,2,-4],[3,-3,1])([1],[0],[1])=  9. ([5,1,-1],[4,2,-4],[3,-3,1])([1],[0],[1])= a So we have demonstrated that ([1],[0],[1]) is an eigenvector with eigenvalue Number Note: the Maple notation for the vector ([1],[2],[3]) is {(:<1,2,3:)} Similarly we can check that ([0],[1],[1]) is an eigenvector with eigenvalue ([1],[1],[0]) is an eigenvector with eigenvalue

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