Question: 6. Let V be a finite dimensional vector space over a field F, and let R. Te C(V). Suppose that S e C(V) is invertible,

6. Let V be a finite dimensional vector space over a field F, and let R. Te C(V). Suppose that S e C(V) is invertible, and that T = SRS-1. Let Kx(T) denote the A-generalized eigensapce of T; and Kx(R) the A-generalized eigensapce of R. 6(a) Prove that x E Kx (T) if and only if Six e Kx(R). [4 marks]6. Let V be a finite dimensional vector space over a field F, and let R, Te S(V). Suppose that S e C(V) is invertible, and that T = SRS-1. Let Kx(T) denote the A-generalized eigensapce of T; and Kx(R) the A-generalized eigensapce of R. 6(b) Prove that dim Kx (T) = dim Kx (R). [4 marks]

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