Page 368 - Schaum's Outline of Differential Equations

ANSWERS TO SUPPLEMENTARY PROBLEMS 351

15.22. Not defined 15.23. Not defined

(b) not defined

15.30. i . Not defined

2
2
15.32. X -1 = 0;X 1 = 1,X 2 = -1 15.33. X -2A, + 13 = 0; \ = 1 + 2-J31,
15.33.
X 2 = 1 - 2-j3i
2
2
15.34. X -2X-1 = 0;X 1= 1 + V2,X 2 =1-V2 15.35. X - 9 = 0; Xj = 3, X 2 = -3
2
2
15.36. X -lCa + 24 = 0;X 1 = 4, X 2 = 6 15.37. (1 - X) (X + 1) = 0; A,! = 1, X 2 = -z, Xg = -z
Each eigenvalue has multiplicity one.

2
15.38. (-X.) (X - 5X.) = 0; ^ = 0, X 2 = 0, Ag = 5
The eigenvalue X = 0 has multiplicity
two,while X = 5 has multiplicity one.

2
2
15.40. (5t - X) (k - 25t ) = 0; A,j = 5r, X 2 = 5r, Xg = -5f 15.41.

CHAPTER 16