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- # 1.a
- a = sample(-20:20, 100, replace = TRUE)
- A = matrix(a, nr = 10, nc = 10)
- # 1.b
- s = sample(3:8, 1)
- b = sample(-20:20, 10*s, replace = TRUE)
- B = matrix(b, nr= s, nc= 10 )
- # 1.c
- c = sample(-20:20, 10*s, replace = TRUE)
- C = matrix(c, nr= 10, nc= s)
- #2a
- B + t(C)
- #2b
- 3*A -5*C %*% B
- #2c
- Ainv=solve(A)
- Ainv %*% A
- round(Ainv %*% A)
- #3a - pabaigti kitus
- det(t(B) %*% B )
- #4
- D = C%*%t(C)
- v = matrix(sample(-20:20, 10), 10, 1)
- solve(A, v)
- solve(D, v) # det=0, negali spresti
- matrix.rank(D)
- DD = cbind(D, v) #prijungti stulpeli v
- DD
- matrix.rank(DD) #R reikalauja kvadratine
- z = matrix(sample(0, 11, replace=TRUE), 1, 11) #sukuriama nuline eilute, kad nepakeisti ranko
- DDD = rbind(DD, z) #prijungia nuline eilute
- matrix.rank(DDD) #isplestines matricos rank ligus 7, originalios 6. rankai nesutampa, reiskia nera sprendimu
- #5
- E = t(B) %*% B
- a = E %*% v
- solve(E, a) #nemoka skaiciuoti tokia
- matrix.rank(E)
- EE = cbind(E,a)
- EEE = rbind(EE,z)
- matrix.rank(EEE) #rankE = rankEEE, be galo sprendimu
- x1 = solveSLE(E,a) #sukurta funkcija
- x2 = solveSLE(E,a)
- round(E %*% x1)
- round(a)
- #6
- Lambda = eigen(E) # ieskome tikriniu reiksmiu
- TR = Lambda$values
- TV = Lambda$vectors #vektoriai normuoti - (isvada)
- TV1 = TV[1:10, 1]
- TV2 = TV[1:10, 10]
- norm(TV1, "2") #tikriname norma "2" - saknies is kvadratu sumos, jeigu = 1, reiskia normuoti
- norm(TV1, "2")
- #vektorius yra tikrinis jeigu tenkinama salyga: Ex=lambda * x
- E%*%TV1
- TR[1]*TV1
- E%*%TV2
- TR[10]*TV2
- #tikrinti
- (E%*%v)/v #nevienodi, tai netikrinis
- (E%*%TV2)/TV2 #vienodi, tai tikrinis
- #pedsakos lygus tikriniai reiksmiu sumai
- matrix.trace(E)
- sum(TR)
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