no 4Metode Gaus

8w+4x-3y-y=12 8w+4x-3y-y=122w+6x+3y-3z=2z = 2w+6x+3y-5z=03w-2x+10y+5y=44 3w-2x+10y+5y=443w-2x-4y+12z=32 3w-2x-4y+12z=32

Segitiga Atasw x y z konstanta

8 4 -3 -1 122 6 3 -5 03 -2 10 5 443 -2 -4 12 32

pengenolan pojok kiri bawah

3 -2 -4 12 323 -2 10 5 440 0 -14 7 -12

matiks menjadi8 4 -3 -1 122 6 3 -5 03 -2 10 5 440 0 -14 7 -12

pengenolan baris 3 colom 1

3 -2 10 5 443 9 4.5 -7.5 00 -11 5.5 12.5 44

matriks menjadi8 4 -3 -1 122 6 3 -5 00 -11 5.5 12.5 440 0 -14 7 -12

pengenolan baris 2 colom 12 6 3 -5 02 1 -0.75 -0.25 30 5 3.75 -4.75 -3

matriks menjadi

8 4 -3 -1 120 5 3.75 -4.75 -30 -11 5.5 12.5 440 0 -14 7 -12

pengenolan baris 3 colom 20 -11 5.5 12.5 440 -11 -8.25 10.45 0 6.60 0 13.75 2.05 37.4

matriks menjadi8 4 -3 -1 120 5 3.75 -4.75 -30 0 13.75 2.05 37.40 0 -14 7 -12

pengenolan baris 4 colom 30 0 -14 7 -120 0 -14 -2.087273 -38.080 0 0 9.087273 26.08

matriks menjadi8 4 -3 -1 120 5 3.75 -4.75 -30 0 13.75 2.05 37.40 0 0 9.087273 26.08

z=26,08/9,087273z= 2.869948

y=(37,4-2,05(2869948))/13,75y= 2.292117

x=(-3+4,75(2,869948)-3,75(2,292117))/5x= 0.407363

w=(12+1(2,869948)+3(2,292117)-4(0,407363))/8w= 2.514606

Segitiga Bawahw x y z

8 4 -3 -12 6 3 -53 -2 10 53 -2 -4 12

Pengenolan pojok kanan atas

Baris 4 8 4 -3 -1- Baris 3 0.4 1.2 0.6 -1

7.6 2.8 -3.6 0

matriks menjadi7.6 2.8 -3.6 0

2 6 3 -53 -2 10 53 -2 -4 12

pengenolan baris ke 2 colom 4

Baris 3 2 6 3 -5- Baris 2 x 3/2 3 -2 10 5

5 4 13 0

matriks menjadi7.6 2.8 -3.6 0

5 4 13 03 -2 10 53 -2 -4 12

pengenolan baris 3 colom 4Baris 2 3 -2 10 5

- Baris 1 x 1/4 1.25 -0.833333 -1.666667 51.75 -1.166667 11.66667 0

matriks menjadi

7.6 2.8 -3.6 05 4 13 0

1.75 -1.166667 11.66667 03 -2 -4 12

pengenolan baris 1 colom 3Baris 3 7.6 2.8 -3.6 0

- Baris 2 x (-11)/5 1.384615 1.107692 3.6 08.984615 3.907692 0 0

matriks menjadi8.984615 3.907692 0 0

5 4 13 01.75 -1.166667 11.66667 0

3 -2 -4 12

pengenolan baris 2 colom 3Baris 4 5 4 13 0

- Baris 3 x (-14)/13,75 1.95 -1.3 13 03.05 5.3 0 0

matriks menjadi8.984615 3.907692 0 0

3.05 5.3 0 01.75 -1.166667 11.66667 0

3 -2 -4 12

pengenolan baris 1 colom 28.984615 3.907692 0 02.248766 3.907692 0 06.735849 0 0 0

matriks menjadi6.735849 0 0 0

3.05 5.3 0 01.75 -1.166667 11.66667 0

3 -2 -4 12

w=16,93801/6,735849w= 2.514606

x=(9,828571-3,05(2,514606))/5,3x= 0.407363

y=(30,66667-1,75(2,514606)+1,16667(0,407363))/11,66667

Y= 2.292117

z=(32-3(2,514606)+2(0,407363)+4(2,292117))/12z= 2.869948

konstanta12

04432

12 Baris 10 - Baris 2 x 1/5

12

120

4432

0 Baris 244 + Baris 344

12444432

44 Baris 313.33333 - Baris 4 x 5/1230.66667

1244

30.6666732

12 Baris 112.18462 + baris 2 x 3,6/1324.18462

24.1846244

30.6666732

44 baris 234.17143 - baris 3 x 13/11,66679.828571

24.184629.82857130.66667

32

24.18462 baris 17.24661 - baris 2 x 3,907692/5,3

16.93801

16.938019.82857130.66667

32

y=(30,66667-1,75(2,514606)+1,16667(0,407363))/11,66667

z=(32-3(2,514606)+2(0,407363)+4(2,292117))/12

no 4metode gaus sidle

w x y z0 0 0 0

1.5 -0.5 3.85 3.4916673.630208 -0.225347 1.520035 2.2282352.461216 0.27644 2.602806 2.9650382.708462 0.266641 2.158271 2.7534152.520208 0.375308 2.342292 2.879932.550697 0.378564 2.270539 2.8489332.518287 0.399412 2.29993 2.8703072.521556 0.401439 2.288667 2.866073

2.51579 0.405464 2.293319 2.8697362.51598 0.406127 2.291563 2.869214

2.514924 0.406922 2.2923 2.8698562.514884 0.407102 2.292027 2.8698052.514685 0.407262 2.292144 2.8699212.514663 0.407307 2.292102 2.869922.514625 0.40734 2.292121 2.8699412.514618 0.407351 2.292114 2.869942

2.51461 0.407358 2.292117 2.8699462.514608 0.40736 2.292116 2.8699472.514607 0.407362 2.292117 2.869948 w2.514606 0.407362 2.292117 2.869948 x2.514606 0.407363 2.292117 2.869948 y2.514606 0.407363 2.292117 2.869948 z

8 4 -3 -1 122 6 3 -5 03 -2 10 5 443 -2 -4 12 32

2.5146060.4073622.2921172.869948

no 4Metode Jacobi

8w+4x-3y-y=122w+6x+3y-5z=03w-2x+10y+5y=443w-2x-4y+12z=32

w 2.514606x 0.407363y 2.292117z 2.869948

8 42 63 -23 -2

w x0 0

1.5 03.4833333333 -0.47777777783.1899305556 0.66252.0099074074 0.40357253092.4586658468 0.22245466822.7594695136 0.34473678092.5286169777 0.45390420112.4270473428 0.3896995846

2.538619655 0.37438337972.5521191283 0.4084260624

2.502326363 0.41358780422.5042800994 0.40108952552.5233274192 0.40327436352.5181707148 0.40893783682.5110308547 0.40765789972.5142369124 0.4059914912.5163847819 0.40709196292.5145701953 0.40771536652.5139844851 0.40724664412.5147987749 0.4071425079

2.514859125 0.40739118292.5145017066 0.40740925762.5145368226 0.40731898822.5146702909 0.40733784572.5146271041 0.40737657962.5145789117 0.40736493182.5146044379 0.40735352022.5146183872 0.4073617741

2.5146048238 0.40736566652.5146014285 0.4073620691

2.514607413 0.40736148792.514607533 0.4073632607

2.5146049987 0.40736327992.5146053892 0.40736262952.5146063187 0.40736279292.5146059643 0.40736305562.5146056426 0.40736295672.5146058418 0.40736287982.5146059306 0.40736294172.5146058299 0.40736296552.5146058114 0.4073629384

2.514605855 0.40736293552.5146058535 0.40736294812.5146058357 0.40736294752.5146058394 0.40736294292.5146058458 0.4073629443

2.514605843 0.4073629462.5146058409 0.40736294522.5146058424 0.4073629447

2.514605843 0.40736294522.5146058422 0.40736294532.5146058421 0.40736294512.5146058424 0.40736294512.5146058424 0.4073629452

-3 -1 123 -5 0

10 5 44-4 12 32

y z0 0

4.4 2.66666666672.6166666667 3.75833333331.3802777778 2.58842592592.2813078704 2.4396932872.6578956404 2.99188786012.2109472495 2.97504119652.1535859039 2.77123783492.3465768294 2.82802509042.3358131689 2.90704703822.2597672603 2.87301337252.2795427878 2.84996364842.3070378277 2.8698639725

2.294001889 2.87645750532.2854278943 2.86771450212.2924791019 2.86708959222.2946775274 2.8710116369

2.291421406 2.87066519622.2911703599 2.8692262672.2925588812 2.86970013222.2924039172 2.87023127982.2918732292 2.86995869672.2920411508 2.8698081592.2922272601 2.86995649992.2921245009 2.86999471242.2920691257 2.86993023522.2921220671 2.86992902912.2921347983 2.86995678312.2921109811 2.8699527433

2.292110467 2.86994269262.2921203399 2.86994656082.2921187049 2.8699501012.2921150232 2.8699479632.2921164107 2.86994700132.2921176557 2.86994810062.2921168588 2.86994830952.2921165082 2.86994783872.2921169025 2.86994785422.2921169714 2.86994804962.2921167986 2.869948012.2921168042 2.86994794052.2921168739 2.86994797152.2921168585 2.86994799482.2921168332 2.86994797832.2921168444 2.86994797242.2921168526 2.86994798052.2921168465 2.86994798152.2921168444 2.86994797812.2921168473 2.86994797842.2921168476 2.86994797972.2921168464 2.86994797942.2921168465 2.86994797892.2921168469 2.86994797922.2921168468 2.86994797932.2921168466 2.8699479792