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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