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Let A be a square 71 X n-matrix and let A be an eigenvalue of A. Recall that the algebraic multiplicity of A in A is the degree m in a factorization of the characteristic polynomial of A 10,405) = det(A t1") = (t \"\"1103 where q(t) is a polynomial with q(A) g 0. The geometric multiplicity of A is the dimension of the subspace EA (A) of R" that consists of all vectors '1.) satisfying A1; = A1). In this problem, we investigate these two multiplicities. 1 (a) The matrix (0 (1)) has one real eigenvalue A = 1. The algebraic multiplicity of A is l 3 and the geometric multiplicity of A is . 1 1 (b) The matrix (0 1) has one real eigenvalue A = 1. The algebraic multiplicity of A is l and the geometric multiplicity of A is 1 (c) The matrix 0 has one real eigenvalue A = 1. The algebraic multiplicity 0 0H0 l'Ilo of A is' and the geometric multiplicity of A is . 1 0 0 (c) The matrix 0 1 1 has one real eigenvalue A = 1. The algebraic multiplicity 0 0 1 of A is and the geometric multiplicity of A is 0 4 1 0 has two eigenvalues A1 and A2. If we order these two 3 (d) The matrix 0 2 3 eigenvalues so that A1