MA232_Test2_Practice_solns

MA232_Test2_Practice_solns - , ~ v 2 = 1- 5 2-3 2 pg.324...

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MA232 Fall 2008 Test 2 Practice Solutions October 7, 2008 1 Variation of Parameters (Euler-Lagrange Method) pg.71 problem 22: y = e - 2 t pg.71 problem 23: y = - 2 e - 2 t + e t pg.71 problem 24: y = e t + e 3 t 2 pg.71 problem 26: y = e - t ln | 1 + e t | - ln | 2 | e - t pg.71 problem 27: y = e - t 2 +1 2 pg.71 problem 28: y = 2 e - t 3 +1 3 pg.71 problem 29: y = 1+ln t t 2 Linear Algebra 2.1 Matrix Operations 2.2 Eigenstuff and Determinants 2.2.1 Determinants 2.2.2 2x2 Eigenvalues and Eigenvectors pg.324 problem 4: λ 1 = - 1 + 2 i , λ 2 = - 1 - 2 i , ~ v 1 = ± 1 - 1 + i 2 ² , ~ v 2 = ± 1 - 1 - i 2 ² pg.324 problem 6: λ 1 = 5, λ 2 = - 5, ~ v 1 = ± 1 5 2 - 3 2
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Unformatted text preview: , ~ v 2 = 1- 5 2-3 2 pg.324 problem 8: 1 =2, 2 =3, ~ v 1 = 1 5 / 3 , ~ v 2 = 1 3 / 2 **remember that your eigenvectors may be o by a factor on both numbers; this is OK. 1 2.2.3 3x3 Eigenvalues pg.324 problem 22: 1 =0, 2 =0, 3 =-1 pg.324 problem 24: 1 =1, 2 =3, 3 =-2 pg.324 problem 28: 1 =1, 2 =1, 3 =1 pg.324 problem 30: 1 =1, 2 =1, 3 =2 2...
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MA232_Test2_Practice_solns - , ~ v 2 = 1- 5 2-3 2 pg.324...

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