(a) Prove that a linear operator T on a finite-dimensional vector space is invertible if
Chapter 5, Problem 8(choose chapter or problem)
(a) Prove that a linear operator T on a finite-dimensional vector space is invertible if and only if zero is not an eigenvalue of T. (b) Let T be an invertible linear operator. Prove that a scalar A is an eigenvalue of T if and only if A~! is an eigenvalue of T- 1 . (c) State and prove results analogous to (a) and (b) for matrices.
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