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  3. suppose t ∈ l(v) a) show that v = imt0 ⊃

Suppose T ∈ L(V) a) Show that V = ImT0 ⊃ ImT1 ⊃ ImT2 ⊃ ... b) Show...

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Advance Math

Suppose T ∈ L(V)

a) Show that V = ImT0 ⊃ ImT1 ⊃ImT2 ⊃ ...

b) Show that if m ≥ 0 is such that ImTm = ImTm +1, then ImTm + k =ImTm + k + 1 for allk ≥ 0.

c) Show that if n = dim V, then ImTn = ImTn +1 = ImTn + 2 = ....

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