ZADANIE 1
Obliczenia dla zadanych wektorów:
S1 Float64:1.0251881368296672e-10
S2 Float64:-1.5643308870494366e-10
S3 Float64: 0.0
S4 Float64:0.0

S1 Float32:-0.4999443
S2 Float32:-0.4543457
S3 Float32: -0.5
S4 Float32:-0.5

Po zamianie wektorów:
S1 Float64:-2.6068806756139725e-9
S2 Float64:-2.950400812551379e-9
S3 Float64: -2.7939677238464355e-9
S4 Float64:-2.7939677238464355e-9

S1 Float32:-0.4999443
S2 Float32:-0.4543457
S3 Float32: -0.5
S4 Float32:-0.5

ZADANIE 2

Macierze randomowe matcond(n,c)
n: 5 c: 10^0
rank(A): 5 cond(A): 1.000e+00
||x_g-x||/||x||:4.0640835625101184e-16
|x_o-x|/|x| promila:1.4895204919483638e-16
n: 5 c: 10^1
rank(A): 5 cond(A): 1.000e+01
||x_g-x||/||x||:1.719950113979703e-16
|x_o-x|/|x| promila:2.2752801345137457e-16
n: 5 c: 10^3
rank(A): 5 cond(A): 1.000e+03
||x_g-x||/||x||:3.2378793712512043e-14
|x_o-x|/|x| promila:4.031977868837404e-14
n: 5 c: 10^7
rank(A): 5 cond(A): 1.000e+07
||x_g-x||/||x||:2.618806509490498e-10
|x_o-x|/|x| promila:1.887266155899674e-10
n: 5 c: 10^12
rank(A): 5 cond(A): 1.000e+12
||x_g-x||/||x||:1.8003817992107833e-5
|x_o-x|/|x| promila:1.6257280225647e-5
n: 5 c: 10^16
rank(A): 4 cond(A): 1.621e+16
||x_g-x||/||x||:0.6942637706115011
|x_o-x|/|x| promila:0.6369559565817718
n: 10 c: 10^0
rank(A): 10 cond(A): 1.000e+00
||x_g-x||/||x||:2.999657430470547e-16
|x_o-x|/|x| promila:2.9790409838967276e-16
n: 10 c: 10^1
rank(A): 10 cond(A): 1.000e+01
||x_g-x||/||x||:3.845925372767128e-16
|x_o-x|/|x| promila:3.2368285245694683e-16
n: 10 c: 10^3
rank(A): 10 cond(A): 1.000e+03
||x_g-x||/||x||:7.41210035468934e-15
|x_o-x|/|x| promila:1.6926732725965497e-14
n: 10 c: 10^7
rank(A): 10 cond(A): 1.000e+07
||x_g-x||/||x||:4.203328697644576e-10
|x_o-x|/|x| promila:4.1300804327589213e-10
n: 10 c: 10^12
rank(A): 10 cond(A): 1.000e+12
||x_g-x||/||x||:9.963567569252528e-6
|x_o-x|/|x| promila:1.7807011075170512e-5
n: 10 c: 10^16
rank(A): 9 cond(A): 9.715e+15
||x_g-x||/||x||:0.17721066056261747
|x_o-x|/|x| promila:0.13231755201148673
n: 20 c: 10^0
rank(A): 20 cond(A): 1.000e+00
||x_g-x||/||x||:6.78962879315599e-16
|x_o-x|/|x| promila:5.266250202865052e-16
n: 20 c: 10^1
rank(A): 20 cond(A): 1.000e+01
||x_g-x||/||x||:5.779561311678614e-16
|x_o-x|/|x| promila:4.0943002132167223e-16
n: 20 c: 10^3
rank(A): 20 cond(A): 1.000e+03
||x_g-x||/||x||:8.3345145680698e-15
|x_o-x|/|x| promila:1.5660836050922383e-14
n: 20 c: 10^7
rank(A): 20 cond(A): 1.000e+07
||x_g-x||/||x||:9.071282657948125e-11
|x_o-x|/|x| promila:1.0664305324712467e-10
n: 20 c: 10^12
rank(A): 20 cond(A): 1.000e+12
||x_g-x||/||x||:3.4271721890648195e-5
|x_o-x|/|x| promila:3.595760054180711e-5
n: 20 c: 10^16
rank(A): 19 cond(A): 5.043e+15
||x_g-x||/||x||:0.034356624813563705
|x_o-x|/|x| promila:0.06885423561204315

Macierze hilberta hilb(n)
n: 2
rank(A): 2, cond(A): 1.928e+01
||x_g-x||/||x||:5.661048867003676e-16
||x_o-x||/||x||:1.4043333874306803e-15
n: 3
rank(A): 3, cond(A): 5.241e+02
||x_g-x||/||x||:8.022593772267728e-15
||x_o-x||/||x||:0.0
n: 4
rank(A): 4, cond(A): 1.551e+04
||x_g-x||/||x||:4.4515459601812086e-13
||x_o-x||/||x||:4.0996530221808757e-13
n: 5
rank(A): 5, cond(A): 4.766e+05
||x_g-x||/||x||:1.6828426299227195e-12
||x_o-x||/||x||:3.2543043465682462e-12
n: 6
rank(A): 6, cond(A): 1.495e+07
||x_g-x||/||x||:2.618913302311624e-10
||x_o-x||/||x||:1.2883031376157472e-10
n: 7
rank(A): 7, cond(A): 4.754e+08
||x_g-x||/||x||:1.1328142969056265e-8
||x_o-x||/||x||:4.032805581748429e-9
n: 8
rank(A): 8, cond(A): 1.526e+10
||x_g-x||/||x||:1.5829979897374446e-7
||x_o-x||/||x||:4.73672307652826e-7
n: 9
rank(A): 9, cond(A): 4.932e+11
||x_g-x||/||x||:9.390769524774878e-6
||x_o-x||/||x||:1.433221949678536e-5
n: 10
rank(A): 10, cond(A): 1.602e+13
||x_g-x||/||x||:0.00010722274297833791
||x_o-x||/||x||:0.0002552291736870214
n: 11
rank(A): 11, cond(A): 5.224e+14
||x_g-x||/||x||:0.0034291876077933874
||x_o-x||/||x||:0.008272388937184324
n: 12
rank(A): 11, cond(A): 1.734e+16
||x_g-x||/||x||:0.15187091684024712
||x_o-x||/||x||:0.26329832655148755
n: 13
rank(A): 11, cond(A): 1.152e+18
||x_g-x||/||x||:2.076284463662164
||x_o-x||/||x||:1.6394342774716664
n: 14
rank(A): 12, cond(A): 6.061e+17
||x_g-x||/||x||:12.87993770619421
||x_o-x||/||x||:27.030176488679782
n: 15
rank(A): 12, cond(A): 6.504e+17
||x_g-x||/||x||:9.800630209388922
||x_o-x||/||x||:32.67484762379888
n: 16
rank(A): 12, cond(A): 3.499e+17
||x_g-x||/||x||:5.656351931681862
||x_o-x||/||x||:6.880132233688196
n: 17
rank(A): 12, cond(A): 5.047e+17
||x_g-x||/||x||:1.9404955954677465
||x_o-x||/||x||:4.230154728971687
n: 18
rank(A): 12, cond(A): 1.019e+18
||x_g-x||/||x||:9.145697825724167
||x_o-x||/||x||:18.835003944216588
n: 19
rank(A): 13, cond(A): 1.133e+18
||x_g-x||/||x||:17.40345631318777
||x_o-x||/||x||:10.509942542100593
n: 20
rank(A): 13, cond(A): 2.538e+18
||x_g-x||/||x||:53.10656030160923
||x_o-x||/||x||:39.73518807228086