# Untitled

Sep 19th, 2019
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1. # 1.a
2. a = sample(-20:20, 100, replace = TRUE)
3. A = matrix(a, nr = 10, nc = 10)
4. # 1.b
5. s = sample(3:8, 1)
6. b = sample(-20:20, 10*s, replace = TRUE)
7. B = matrix(b, nr= s, nc= 10 )
8. # 1.c
9. c = sample(-20:20, 10*s, replace = TRUE)
10. C = matrix(c, nr= 10, nc= s)
11.
12. #2a
13. B + t(C)
14. #2b
15. 3*A -5*C %*% B
16. #2c
17. Ainv=solve(A)
18. Ainv %*% A
19. round(Ainv %*% A)
20.
21. #3a - pabaigti kitus
22. det(t(B) %*% B )
23.
24. #4
25.
26. D = C%*%t(C)
27. v = matrix(sample(-20:20, 10), 10, 1)
28. solve(A, v)
29. solve(D, v) # det=0, negali spresti
30.
31. matrix.rank(D)
32. DD = cbind(D, v) #prijungti stulpeli v
33. DD
35. z = matrix(sample(0, 11, replace=TRUE), 1, 11) #sukuriama nuline eilute, kad nepakeisti ranko
36. DDD = rbind(DD, z) #prijungia nuline eilute
37. matrix.rank(DDD) #isplestines matricos rank ligus 7, originalios 6. rankai nesutampa, reiskia nera sprendimu
38.
39. #5
40. E = t(B) %*% B
41. a = E %*% v
42. solve(E, a) #nemoka skaiciuoti tokia
43. matrix.rank(E)
44. EE = cbind(E,a)
45. EEE = rbind(EE,z)
46. matrix.rank(EEE) #rankE = rankEEE, be galo sprendimu
47.
48. x1 = solveSLE(E,a) #sukurta funkcija
49. x2 = solveSLE(E,a)
50. round(E %*% x1)
51. round(a)
52.
53. #6
54. Lambda = eigen(E) # ieskome tikriniu reiksmiu
55. TR = Lambda\$values
56. TV = Lambda\$vectors #vektoriai normuoti - (isvada)
57. TV1 = TV[1:10, 1]
58. TV2 = TV[1:10, 10]
59. norm(TV1, "2") #tikriname norma "2" - saknies is kvadratu sumos, jeigu = 1, reiskia normuoti
60. norm(TV1, "2")
61.
62. #vektorius yra tikrinis jeigu tenkinama salyga: Ex=lambda * x
63. E%*%TV1
64. TR[1]*TV1
65.
66. E%*%TV2
67. TR[10]*TV2
68. #tikrinti
69. (E%*%v)/v #nevienodi, tai netikrinis
70.
71. (E%*%TV2)/TV2 #vienodi, tai tikrinis
72. #pedsakos lygus tikriniai reiksmiu sumai
73. matrix.trace(E)
74. sum(TR)
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