=+8.9. 8.5 1 Show for an irreducible chain that (8.27) has a nontrivial solution if and only

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=+8.9. 8.5 1 Show for an irreducible chain that (8.27) has a nontrivial solution if and only if there exists a nontrivial, bounded sequence {x;} (not necessarily nonnega-

tive) satisfying x, = E, . , P ;; x ;, i +i .. (See the remark following the proof of Theorem 8.5.)

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