Given that L = b1 b2 b3 bn1 bn c1 0 0

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Given that L =

⎜⎜⎜⎜⎜⎝

b1 b2 b3 · · · bn−1 bn c1 0 0 · · · 0 0 0 c2 0 · · · 0 0

...

... ...

. . .

...

...

0 0 0 · · · cn−1 0

⎟⎟⎟⎟⎟⎠

, where bi ≥ 0, 0 < ci ≤ 1, and at least two successive bi are strictly positive, prove that p(λ) = 1, if λ is an eigenvalue of L, where p(λ) =

b1

λ +

b2c1

λ2 +· · ·+

bnc1c2 . . . cn−1

λn

.

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258

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