366lab11

366lab11 - >> A=[0,-1;-2,1] >> [B,D]=eig(A)...

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1. 2. a.
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-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 T D 3. T =3 , D=1 (T^2-4D)^0.5 = 5^0.5 < 3
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x1 ' = - x2 x2 ' = x1 + 3 x2 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 x1 x2 They move away from the origin. a. The origin is a source. b. The solutions do not spiral out as they move away from the origin. 4. >> A=[0,-1;1,3] >> [B,D]=eig(A)
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B = -0.9342 0.3568 0.3568 -0.9342 D = 0.3820 0 0 2.6180 Eigenvalues are 0.3820 and 2.6180. Eigenvectors are (-0.9342,0.3568) and (0.3568,-0.9342). 5. 6. T =-3 , D=2 (T^2-4D)^0.5 = 1 > -3
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x1 ' = - x2 x2 ' = 2 x1 - 3 x2 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 x1 x2 All solutions converge to the origin. a. The origin is a sink. b. The solutions do not spiral in. >> A=[0,-1;2,-3] >> [B,D]=eig(A) Eigenvalues are -1 and -2. Eigenvectors are (0.7071,0.7071) and (0.4472,0.8944). 7. T = 1 , D=-2
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x1 ' = - x2 x2 ' = - 2 x1 + 1 x2 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 x1 x2 a. The origin is a saddle. b. The solutions do not spiral in or out.
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Unformatted text preview: >> A=[0,-1;-2,1] >> [B,D]=eig(A) Eigenvalues are -1 and 2. Eigenvectors are (-0.7071,-0.7071) and (0.4472,-0.8944). 8. a. T= -1, D = 1 x1 ' = - x2 x2 ' = x1 - x2-4-3-2-1 1 2 3 4-4-3-2-1 1 2 3 4 x1 x2 Eigenvalues are -0.5000 + 0.8660i and -0.5000 - 0.8660i. Eigenvectors are (0.7071, 0.3536 - 0.6124i) and (0.7071, 0.3536 + 0.6124i). b. T = 1, D = 0.5 Eigenvalues are 0.5000 + 0.5000i and 0.5000 - 0.5000i. x1 ' = - x2 x2 ' = 0.5 x1 + 1 x2-4-3-2-1 1 2 3 4-4-3-2-1 1 2 3 4 x1 x2 Eigenvectors are (0.8165 , -0.4082 - 0.4082i) and (0.8165 , -0.4082 + 0.4082i). c. T = 0, D = 1 Eigenvalues are 1.0000i and 1.0000i. x1 ' = - x2 x2 ' = x1 -4-3-2-1 1 2 3 4-4-3-2-1 1 2 3 4 x1 x2 Eigenvectors are (0.7071 , - 0.7071 i) and (0.7071 , 0.7071i)....
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This note was uploaded on 05/15/2011 for the course MA 366 taught by Professor Cho during the Spring '08 term at Purdue.

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366lab11 - >> A=[0,-1;-2,1] >> [B,D]=eig(A)...

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