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Unformatted text preview: , , , 3 , 3 ,-5. When we use multiplicities and include complex roots, if any, then a polynomial of degree n has exactly n roots. It turns out that matrices A and B related by B = P-1 AP for some invertible matrix P share many important properties. Such matrices are said to be similar . FACT. Similar matrices have the same characteristic polynomial and so have the same eigenvalues with the same multiplicities. EXAMPLE, IF TIME. Analyze the long-term behavior of the system dened by x k +1 = A x k when A = "-1 / 2 1 3 / 2 # and x = " 1 10 # . HOMEWORK: SECTION 5.2...
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