[線代] 線代(10)

[PttFund (批踢踢基金只進不出)]

If V is a finite dimensional vector space, T: V ---> V is a
linear transformation such that T^3 - 3T^2 + 3T - I = O, where
O: V ---> V, O(v) = 0 for all v in V.

(1) Show that there is a v≠0 in V such that T(v) = v.

(2) Show that T is invertible.

              1  1  0
(3) Let A = ( 0  1  1 ).  Show that A is invertible, and express
              0  0  1
    A^{-1} as a polynomial in A with real coefficients.

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，你有摳摳ㄋㄟ
可憐可憐我吧，施捨一點吧
請到(P)LAY-->(P)AY-->(0)GIVE-->PttFund-->吧

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