edvinsav

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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
  34. matrix.rank(DD) #R reikalauja kvadratine
  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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