Suppose thal we wish to extend the method described for finding one generalized eigenvector to finding two (or more) generalized eigenvectors. Let's look at the case where has multiplicity 3 but has only one linearly independent eigenvector io. First. we find ₁ by the method described in this section. Then we find ₂  such that

(We continue in this fashion to obtainfor r < m . where m is the multiplicity of and r is the number of "missing" eigenvectors for .)

(a) Show that

are solutions of given that and has multiplicity 3 and r = 2.

(b) Show that the vectorsvand are linearly independent.

(c) Solve

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(A – AI)ūz = üj. or (A AI)üz = v