Question: Problem 2. Let X be a nite dimensional linear space and T : X > X a linear operator. (a) Prove, without using determinants. that

Problem 2. Let X be a nite dimensional linear space and T : X > X a linear operator. (a) Prove, without using determinants. that I) is an eigenvalue of T if and only if T is not invertible. (b) Suppose that T is invertible. Prove that if a. is an eigenvalue of T. then of] is an eigenvalue of T' 1

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