Question: 4 1 2 5 *3 0 2 ,4 6 8 (1) (30 points) Set A = 0 0 4 l 2 0 0 0 4

4 1 2 5 *3 0 2 ,4 6 8 (1) (30 points) Set A = 0 0 4 l 2 0 0 0 4 0 00012 (a) Find the characteristic polynomial for A; and nd all the eigenvalues for A. (b) Find the algebraic multiplicity and geometric multiplicity for each eigenvalue for A' (c) Is A diagonalizable? (Explain) 1 (2) (40 points) )Let B denote a 3 X 3 matrix. Suppose that v1: 1 , 1 v2 = 1 V3=|: 3 A1_ 7 A2 *1 A Compute 391. are eigenvectors for B with associated eigenvalues llwwm *5 respectively. 2 *2 ,1 (3) (40 points) Find an eigenbasis for C = 3 5 2
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