Lab11 - -0.9717 -0.0000 0.6281 D =-3.0000 0 0 5.0000 0 0...

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Exercise 1 A = 1 -1 4 3 2 -1 2 1 -1 [P,D]=eig(A) P = 0.4082 0.5774 0.2357 0.8165 -0.5774 -0.9428 0.4082 -0.5774 -0.2357 D = 3.0000 0 0 0 -2.0000 0 0 0 1.0000 R = 11.0227 0 0 0 -5.1962 0 0 0 14.8492 E=P*R E = 4.5000 -3.0000 3.5000 9.0000 3.0000 -14.0000 4.5000 3.0000 -3.5000 Exercise 2 B = 4 -3 -7 8 [P,D]=eig(B) P = -0.7071 0.3939 -0.7071 -0.9191 D = 1 0 0 11 Eigen vectors appear as columns of P 1 AND 11 ARE EIGEN VALUES OF B R = -7.7782 0 0 11.4237 E=P*R
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E = 5.5000 4.5000 5.5000 -10.5000 Solution = [x; y; z]= E*[exp(1*t); exp(11*t)] Exercise 3 C = 7 1 -4 4 -2 -2 2 4 -1 [P,D]=eig(C) P = 0.8111 -0.5307 0.4082 0.3244 -0.1516 -0.4082 0.4867 -0.8339 0.8165 D = 5.0000 0 0 0 1.0000 0 0 0 -2.0000 Eigen vectors appear as columns of P 5,1, -2 ARE EIGEN VALUES OF C R = 12.7691 0 0 0 2.1985 0 0 0 -10.2645 E=P*R E = 10.3571 -1.1667 -4.1905 4.1429 -0.3333 4.1905 6.2143 -1.8333 -8.3810 Solution = [x; y; z]= E*[exp(5*t); exp(8*t); exp(-4*t)] Exercise 4 D 1 = 12 -7 4 6 -1 1 -12 12 -7 [P,D]=eig(D 1 ) P = 0.2024 0.7071 0.2617 -0.1215 0.7071 0.7328
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Unformatted text preview: -0.9717 -0.0000 0.6281 D =-3.0000 0 0 5.0000 0 0 2.0000 Eigen vectors appear as columns of P-3, 5, 2 are Eigen values of D R = 27.7855 0 0 -52.7384 0 0 82.7882 E=P*R E = 5.6250 -37.2917 21.6667-3.3750 -37.2917 60.6667-27.0000 0.0000 52.0000 Solution = [x; y; z]= E*[exp(-3*t); exp(5*t); exp(2*t)] Exercise 5 F = 0 0 1 0 0 0 1 25 18 0 12 40 0 [P,D]=eig(F) P = 0.0849 0.2169 0.0849 0.2169 0.1131 -0.1085 0.1131 -0.1085 0.5940 0.8677 -0.5940 -0.8677 0.7920 -0.4339 -0.7920 0.4339 D = 7.0000 0 0 0 4.0000 0 0 0 -7.0000 0 0 0 -4.000 Eigen vectors appear as collums of P 7, 4, -7, -4 are Eigen values of F R = 104.2294 0 0 0 47.3549 0 0 0 72.5473 0 0 0 -10.4768 E=P*R E = 8.8442 10.2727 6.1558 -2.2727 11.7922 -5.1364 8.2078 1.1364 61.9091 41.0909 -43.0909 9.0909 82.5455 -20.5455 -57.4545 -4.5455 Solution = [x; y; z; w]= E*[exp(7*t); exp(4*t); exp(-7*t); exp(-4*t)]...
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This note was uploaded on 04/23/2008 for the course MATH 2373 taught by Professor Miracle during the Spring '08 term at Minnesota.

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Lab11 - -0.9717 -0.0000 0.6281 D =-3.0000 0 0 5.0000 0 0...

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