2 -233 0 0 0 -68 9 50 30 18 -38 -49 7 36 22 12 -27 -77 10 57 33 20 -42 Finding u,(x). Let A= -94 12 69 41 24 -51 -107 14 78 45 29 -58 -110 14 81 46 28 -58 Compute AJ61. That shows you an element of the spectrum. Find the geometric multiplicity of the element you found in 0. Let C = E, of size 6x1. Let 1 -68 -609-1447 -3291 -7313 49-165 427 -1007 -2277 -5037 -77 -265 -701 -1687 -3883 -8721 M =(C AC APC APC AC AC AC)= -94 -321 -847 -2039 -4701 -10581 0 -107 -369 -981 -2375 -5499-12417 0-110 -383 -10292517 -5883 -13395 10000 4 28 0 1 0 0 0 -16 -108 25 00100 159 of size 6x7. This reduces to This provides you 000 10-19 -108 OOOO 1 7 30 0 0 0 0 0 0 0 with a solution to the equation: AC = aC+BAC+c^C+dAC+eAC which in turn provides you with the lowest degree polynomial of A that annihilates C (sends it to 0). Find this lowest degree polynomial p(x). This polynomial has to be a divisor of u.(x). As it turns out in this case, it is (x). Find Xx(x), 2(A) and det A. 2 -233 0 0 0 -68 9 50 30 18 -38 -49 7 36 22 12 -27 -77 10 57 33 20 -42 Finding u,(x). Let A= -94 12 69 41 24 -51 -107 14 78 45 29 -58 -110 14 81 46 28 -58 Compute AJ61. That shows you an element of the spectrum. Find the geometric multiplicity of the element you found in 0. Let C = E, of size 6x1. Let 1 -68 -609-1447 -3291 -7313 49-165 427 -1007 -2277 -5037 -77 -265 -701 -1687 -3883 -8721 M =(C AC APC APC AC AC AC)= -94 -321 -847 -2039 -4701 -10581 0 -107 -369 -981 -2375 -5499-12417 0-110 -383 -10292517 -5883 -13395 10000 4 28 0 1 0 0 0 -16 -108 25 00100 159 of size 6x7. This reduces to This provides you 000 10-19 -108 OOOO 1 7 30 0 0 0 0 0 0 0 with a solution to the equation: AC = aC+BAC+c^C+dAC+eAC which in turn provides you with the lowest degree polynomial of A that annihilates C (sends it to 0). Find this lowest degree polynomial p(x). This polynomial has to be a divisor of u.(x). As it turns out in this case, it is (x). Find Xx(x), 2(A) and det A