(Fredholm Alternative Theorem) Let T : V V be a linear operator on an n-dimensional

Chapter 8, Problem 10

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(Fredholm Alternative Theorem) Let T : V V be a linear operator on an n-dimensional vector space. Prove that exactly one of the following statements holds: (i) The equation T(x) = b has a solution for all vectors b in V. (ii) Nullity of T > 0.

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