258 4. For each of the following matrices A Є Mnxn (F), (i) Determine all the eigenvalues of A. (ii) For each eigenvalue A of A, find the set of eigenvectors correspond- ing to A. (iii) If possible, find a basis for F" consisting of eigenvectors of A. (iv) If successful in finding such a basis, determine an invertible matrix Q and a diagonal matrix D such that Q¹AQ = D. Chap. 5 Diagonalization 1 2 (a) A= for F = R 3 2 0 -2 (b) A = = 1 -1 for F = R 2 2 5 (c) A= (2 ½) for F = C 2 0 -1 (d) A 4 1 -4 for FR 0 -1

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