4. Let V be a vector space over C and let L : V → V be a linear transformation. (a) State the definition of an eigenvector of L. (b) Let A e C be arbitrary. State the definition of V,, the A-eigenspace of L, and prove that it is a subspace of V. (c) Find the characteristic polynomial Pa(t) of the matrix A given below, and then the eigen- values of A. -1 -1 2 A = 2 2 1 -1

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.