spl-gauss jordan.xlsx

document.xlsx - invers - hal. 1 dari 25

SOAL TUGAS SISTEM PERSAMAAN LINIER

[ A ] { b } { b } { X }nomor 1x – 3y – 2z = 6 1 -3 -2 6 -2 1.7143 0.1429 6 12x – 4y – 3z = 8 2 -4 -3 8 -1 0.2857 -0.1429 8 -3-3x + 6y + 8z = -5 -3 6 8 -5 0 0.4286 0.2857 -5 2

nomor 2x + 2y + z = 3 1 2 1 3 0.25 0 0.25 3 22x + 5y – z = -4 2 5 -1 -4 0.0357 0.1429 -0.1071 -4 -13x – 2y – z = 5 3 -2 -1 5 0.6786 -0.2857 -0.0357 5 3

nomor 3x + 1/2 y + 1/3 z = 1 1 1/2 1/3 1 9 -36 30 1 91/2x + 1/3y + 1/4z = 0 1/2 1/3 1/4 0 -36 192 -180 0 -361/3x + 1/4y + 1/5z = 0 1/3 1/4 1/5 0 30 -180 180 0 30

nomor 4w + 2x – 12y + 8z = 27 1 2 -12 8 27 0.0356 0.1345 -0.0249 0.0362 27 35w + 4x + 7y – 2z = 4 5 4 7 -2 4 0.059 0.0566 -0.0289 -0.0715 4 -2-3w + 7x + 9y + 5z = 11 -3 7 9 5 11 -0.0506 0.0098 0.0652 0.0329 11 16w – 12x – 8y + 3z = 49 6 -12 -8 3 49 0.0299 -0.0163 0.1081 0.0626 49 5

nomor 533x + 16y + 72z = 359 33 16 72 359 -9.6667 -2.6667 -32 359 -6939.667-24x – 10y – 57z = 281 -24 -10 -57 281 8 2.5 25.5 281 5742-8x – 4y – 17z = 85 -8 -4 -17 85 2.6667 0.6667 9 85 1909.6667

[ A-1 ]


nomor 61,7x + 2,3y – 1,5z = 2,35 1.7 2.3 -1.5 2.35 0.2092 0.0176 0.2315 2.35 1.11,1x + 1,6y – 1,9z = -0,94 1.1 1.6 -1.9 -0.94 0.7967 -0.7756 -0.1857 -0.94 2.12,7x – 2,2y + 1,5z = 2,7 2.7 -2.2 1.5 2.7 0.792 -1.1692 -0.0223 2.7 2.9

nomor 7x + 1/2y + 1/3z + 1/4z = 1 1 1/2 1/3 1/4 1 16 -120 240 -140 1 161/2x + 1/3y + 1/4z + 1/5z = 0 1/2 1/3 1/4 1/5 0 -120 1200 -2700 1680 0 -1201/3x + 1/4y + 1/5z + 1/6z = 0 1/3 1/4 1/5 1/6 0 240 -2700 6480 -4200 0 2401/4x + 1/5y + 1/6z + 1/7z = 0 1/4 1/5 1/6 1/7 0 -140 1680 -4200 2800 0 -140

nomor 83x + 2y – 5z = 8 3 2 -5 8 0.0526 0.1579 0.0526 8 1.68421055x – 2y + 3z = 5 5 -2 3 5 -0.3026 0.0921 0.4474 5 2.0657895x + 4y – 2z = 9 1 4 -4 9 -0.2895 0.1316 0.2105 9 0.2368421

nomor 9–x + y + 2z = 2 -1 1 2 2 -0.7 0.2 0.3 2 13x – y + z = 6 3 -1 1 6 -1.3 -0.2 0.7 6 -1–x + 3y + 4z = 4 -1 3 4 4 0.8 0.2 -0.2 4 2

nomor 104y + 3z = 13 0 4 3 13 13x – 2y + z = 3 1 -2 1 3 33x + 5y = 11 3 5 0 11 11pertukaran baris

1 -2 1 3 0.3333 0.2222 -0.1111 3 2


3 5 0 11 -0.2 0.0667 0.0667 11 10 4 3 13 0.2667 -0.0889 0.2444 13 3

nomor 11–x + y + 2z = 0 -1 1 2 0 03x + 4y + z = 0 3 4 1 0 02x + 5y + 3z = 0 2 5 3 0 0

nomor 124x – y + z = 0 4 -1 1 0 0.234 0.1277 -0.0213 0 0x + 2y – z = 0 1 2 -1 0 -0.1702 0.3617 0.1064 0 03x + y + 5z = 0 3 1 5 0 -0.1064 -0.1489 0.1915 0 0

nomor 13x + y + z = -1 1 1 1 -1 1 0 -1 -1 -24y + 6z = 6 0 4 6 6 0 -0.5 3 6 0y + z = 1 0 1 1 1 0 0.5 -2 1 1

nomor 143y – 4z = 1 0 3 -4 1 19x – 4y + z = 4 9 -4 1 4 4x + y + z = 15 1 1 1 15 15pertukaran baris

9 -4 1 4 0.0921 0.1711 0.0658 4 31 1 1 15 -0.0526 0.4737 0.1053 15 70 3 -4 1 -0.0395 0.3553 -0.1711 1 5

nomor 15


2x + 2y – 4z = -1 2 2 -4 -1 -0.14 0.2 -0.32 -1 0.53y + 2z = 9 0 3 2 9 0.16 0.2 0.08 9 2-4x + y + 3z = 4,5 -4 1 3 4.5 -0.24 0.2 -0.12 4.5 1.5

nomor 16-3x + 3y + 7z = 4 -3 3 7 4 4x – y + 2z = 3 1 -1 2 3 34x – 4y + z = 5 4 -4 1 5 5

nomor 173x – 12y = 6 3 -12 0 6 6-7x + 28y = -14 -7 28 0 -14 -145x – 20y = 10 5 -20 0 10 10

nomor 182y – z = 1 0 2 -1 1 14x – 10y + 3z = 5 4 -10 3 5 53x – 3y = 6 3 -3 0 6 6

nomor 196x – 6y + 2z = 28 6 -6 2 28 28 -x + 9y – 3z = -10 -1 9 -3 -10 -10 1/4x – y + 1/3z = 5/3 1/4 -1 1/3 1 2/3 1 2/3

nomor 203x + 4y + 6z = 1 3 4 6 1 1


-2x + 8y – 4z = 2 -2 8 -4 2 24x – 8y + 8z = -2 4 -8 8 -2 -2

nomor 215x + 3y = 22 5 3 0 22 22-4x + 7y = 20 -4 7 0 20 209x – 2y = 15 9 -2 0 15 15

nomor 224y + 7z = -13 0 4 7 -13 -135x – 3y + 4z = - 23 5 -3 4 -23 -23-x + 2y – 8z = 29 -1 2 -8 29 29pertukaran baris

5 -3 4 -23 0.2383 0.1917 0.0829 -23 -1-1 2 -8 29 0.0363 0.1813 0.1865 29 20 4 7 -13 -0.0207 -0.1036 0.0363 -13 -3

nomor 236x + 18y – 4y = 20 6 18 -4 20 -0.0295 0.3227 0.3 20 4-x – 3y + 8z = 4 -1 -3 8 4 0.0705 -0.0773 -0.1 4 05x + 5y – 9z = 11 5 5 -9 11 0.0227 0.1364 0 11 1

nomor 24w + x + y = 3 1 1 1 0 3 0.5714 -0.102 0.0306 0.3571 3 2-3w – 17x + y + 2z = 1 -3 -17 1 2 1 0.0357 -0.0153 -0.0204 -0.0714 1 04w – 17x + 8y – 5z = 1 4 -17 8 -5 1 0.3929 0.1173 -0.0102 -0.2857 1 1-5x – 2y + z = 1 0 -5 -2 1 1 0.9643 0.1582 -0.1224 0.0714 1 3


nomor 25w – x + 3y – 3z = 3 1 -1 3 -3 3 3-5w + 2x – 5y + 4z =-5 -5 2 -5 4 -5 -5-3w – 4x + 7y – 2z = 7 -3 -4 7 -2 7 72w + 3x + y – 11z = 1 2 3 1 -11 1 1

document.xlsx - gauss - hal. 7 dari 25

SOAL TUGAS SISTEM PERSAMAAN LINIER [ A ] { b } eliminasi ke-1

nomor 1-x + y - 2z = 2 3 -1 1 6 3 -1 1 63x - y + z = 6 -1 3 4 4 0 2.66667 4.33333 6-x + 3y + 4z = 4 -1 1 -2 2 0 0.66667 -1.66667 4

nomor 2x + 2y + z = 3 1 2 1 3 1 2 1 32x + 5y – z = -4 2 5 -1 -4 0 1 -3 -103x – 2y – z = 5 3 -2 -1 5 0 -8 -4 -4

nomor 3x + 1/2 y + 1/3 z = 1 1 1/2 1/3 1 1 0.5 0.33333 11/2x + 1/3y + 1/4z = 0 1/2 1/3 1/4 0 0 0.08333 0.08333 -0.51/3x + 1/4y + 1/5z = 0 1/3 1/4 1/5 0 0 0.08333 0.08889 -0.33333

nomor 4w + 2x – 12y + 8z = 27 1 2 -12 8 27 1 2 -12 8 275w + 4x + 7y – 2z = 4 5 4 7 -2 4 0 -6 67 -42 -131-3w + 7x + 9y + 5z = 11 -3 7 9 5 11 0 13 -27 29 926w – 12x – 8y + 3z = 49 6 -12 -8 3 49 0 -24 64 -45 -113

nomor 533x + 16y + 72z = 359 33 16 72 359 33 16 72 359-24x – 10y – 57z = 281 -24 -10 -57 281 0 1.63636 -4.63636 542.091-8x – 4y – 17z = 85 -8 -4 -17 85 0 -0.12121 0.45455 172.03


eliminasi ke-2 eliminasi ke-3 eliminasi ke-4

3 -1 1 6 3 0 2.625 8.25 3 0 0 10.63640 2.66667 4.33333 6 0 2.66667 4.33333 6 0 2.66667 0 9.939390 0 -2.75 2.5 0 0 -2.75 2.5 0 0 -2.75 2.5

1 2 1 3 1 0 7 23 1 0 0 20 1 -3 -10 0 1 -3 -10 0 1 0 -10 0 -28 -84 0 0 -28 -84 0 0 -28 -84

1 0.5 0.33333 1 1 0 -0.16667 4 1 0 0 90 0.08333 0.08333 -0.5 0 0.08333 0.08333 -0.5 0 0.08333 0 -30 0 0.00556 0.16667 0 0 0.00556 0.16667 0 0 0.00556 0.16667

1 2 -12 8 27 1 2 -12 8 27 1 0 10.3333 -6 -16.66670 -6 67 -42 -131 0 -6 67 -42 -131 0 -6 67 -42 -1310 0 118.167 -62 -191.833 0 0 118.167 -62 -191.833 0 0 118.167 -62 -191.8330 0 -204 123 411 0 0 0 15.9647 79.8237 0 0 0 15.9647 79.8237

33 16 72 359 33 0 117.333 -4941.44 33 0 0 -2290090 1.63636 -4.63636 542.091 0 1.63636 -4.63636 542.091 0 1.63636 0 93960 0 0.11111 212.185 0 0 0.11111 212.185 0 0 0.11111 212.185


hasilx y z1 0 0 3.54545 z = -0.909090 1 0 3.72727 y = 3.727270 0 1 -0.90909 x = 3.54545

1 0 0 0.66667 z = 30 1 0 -1 y = -10 0 1 3 x = 2

1 0 0 9 z = 300 1 0 -36 y = -360 0 1 30 x = 9

w x y z1 0 0 -0.57828 0.1086 1 0 0 0 3 1 0 0 0 30 -6 0 -6.84626 -22.2313 0 -6 0 0 12 0 1 0 0 -20 0 118.167 -62 -191.833 0 0 118.167 0 118.167 0 0 1 0 10 0 0 15.9647 79.8237 0 0 0 15.9647 79.8237 0 0 0 1 5

1 0 0 -6939.67 z = 1909.670 1 0 5742 y = 57420 0 1 1909.67 x = -6939.67


nomor 61,7x + 2,3y – 1,5z = 2,35 1.7 2.3 -1.5 2.35 1.7 2.3 -1.5 2.351,1x + 1,6y – 1,9z = -0,94 1.1 1.6 -1.9 -0.94 0 0.11176 -0.92941 -2.460592,7x – 2,2y + 1,5z = 2,7 2.7 -2.2 1.5 2.7 0 -5.85294 3.88235 -1.03235

nomor 7x + 1/2y + 1/3z + 1/4z = 1 1 1/2 1/3 1/4 1 1 0.5 0.33333 0.25 11/2x + 1/3y + 1/4z + 1/5z = 0 1/2 1/3 1/4 1/5 0 0 0.08333 0.08333 0.075 -0.51/3x + 1/4y + 1/5z + 1/6z = 0 1/3 1/4 1/5 1/6 0 0 0.08333 0.08889 0.08333 -0.333331/4x + 1/5y + 1/6z + 1/7z = 0 1/4 1/5 1/6 1/7 0 0 0.075 0.08333 0.08036 -0.25

nomor 83x + 2y – 5z = 8 3 2 -5 8 3 2 -5 85x – 2y + 3z = 5 5 -2 3 5 0 -5.33333 11.3333 -8.33333x + 4y – 2z = 9 1 4 -4 9 0 3.33333 -2.33333 6.33333pertukaran baris

3 2 -5 85 -2 3 51 4 -4 9

nomor 9–x + y + 2z = 2 -1 1 2 2 -1 1 2 23x – y + z = 6 3 -1 1 6 0 2 7 12–x + 3y + 4z = 4 -1 3 4 4 0 2 2 2

nomor 104y + 3z = 13 0 4 3 13


1.7 2.3 -1.5 2.35 1.7 0 17.6263 52.9863 1.7 0 0 1.870 0.11176 -0.92941 -2.46059 0 0.11176 -0.92941 -2.46059 0 0.11176 0 0.234710 0 -44.7895 -129.889 0 0 -44.7895 -129.889 0 0 -44.7895 -129.889

1 0.5 0.33333 0.25 1 1 0.5 0.33333 0.25 1 1 0 -0.16667 -0.2 40 0.08333 0.08333 0.075 -0.5 0 0.08333 0.08333 0.075 -0.5 0 0.08333 0.08333 0.075 -0.50 0 0.00556 0.00833 0.16667 0 0 0.00556 0.00833 0.16667 0 0 0.00556 0.00833 0.166670 0 0.00833 0.01286 0.2 0 0 0 0.00036 -0.05 0 0 0 0.00036 -0.05

3 2 -5 8 3 0 -0.75 4.875 3 0 0 5.052630 -5.33333 11.3333 -8.33333 0 -5.33333 11.3333 -8.33333 0 -5.33333 0 -11.01750 0 4.75 1.125 0 0 4.75 1.125 0 0 4.75 1.125

-1 1 2 2 -1 0 -1.5 -4 -1 0 0 -10 2 7 12 0 2 7 12 0 2 0 -20 0 -5 -10 0 0 -5 -10 0 0 -5 -10


1 0 0 1.1 z = 2.90 1 0 2.1 y = 2.10 0 1 2.9 x = 1.1

1 0 0 0.05 9 1 0 0 0 16 1 0 0 0 160 0.08333 0 -0.05 -3 0 0.08333 0 0 -10 0 1 0 0 -1200 0 0.00556 0.00833 0.16667 0 0 0.00556 0 1.33333 0 0 1 0 2400 0 0 0.00036 -0.05 0 0 0 0.00036 -0.05 0 0 0 1 -140

1 0 0 1.68421 z = 0.23684 0 0 0.99071 z = 0.236840 1 0 2.06579 y = 2.06579 8.94737 0 18.4834 y = 2.065790 0 1 0.23684 x = 1.68421 0 -0.02233 -0.00529 x = 1.68421

1 0 0 10 1 0 -10 0 1 2


x – 2y + z = 3 1 -2 1 33x + 5y = 11 3 5 0 11pertukaran baris

1 -2 1 3 1 -2 1 33 5 0 11 0 11 -3 20 4 3 13 0 4 3 13

nomor 11–x + y + 2z = 0 -1 1 2 03x + 4y + z = 0 3 4 1 02x + 5y + 3z = 0 2 5 3 0

nomor 124x – y + z = 0 4 -1 1 0 4 -1 1 0x + 2y – z = 0 1 2 -1 0 0 2.25 -1.25 03x + y + 5z = 0 3 1 5 0 0 1.75 4.25 0

nomor 13x + y + z = -1 1 1 1 -1 1 1 1 -14y + 6z = 6 0 4 6 6 0 4 6 6y + z = 1 0 1 1 1 0 1 1 1

nomor 143y – 4z = 1 0 3 -4 19x – 4y + z = 4 9 -4 1 4x + y + z = 15 1 1 1 15pertukaran baris

9 -4 1 4 9 -4 1 41 1 1 15 0 1.44444 0.88889 14.5556


1 -2 1 3 1 0 0.45455 3.36364 1 0 0 20 11 -3 2 0 11 -3 2 0 11 0 110 0 4.09091 12.2727 0 0 4.09091 12.2727 0 0 4.09091 12.2727

4 -1 1 0 4 0 0.44444 0 4 0 0 00 2.25 -1.25 0 0 2.25 -1.25 0 0 2.25 0 00 0 5.22222 0 0 0 5.22222 0 0 0 5.22222 0

1 1 1 -1 1 0 -0.5 -2.5 1 0 0 -20 4 6 6 0 4 6 6 0 4 0 00 0 -0.5 -0.5 0 0 -0.5 -0.5 0 0 -0.5 -0.5

9 -4 1 4 9 0 3.46154 44.3077 9 0 0 270 1.44444 0.88889 14.5556 0 1.44444 0.88889 14.5556 0 1.44444 0 10.1111


1 0 0 2 z = 30 1 0 1 y = 10 0 1 3 x = 2

1 0 0 0 z = 00 1 0 0 y = 00 0 1 0 x = 0

1 0 0 -2 z = 10 1 0 0 y = 00 0 1 1 x = -2

1 0 0 3 z = 50 1 0 7 y = 7


0 3 -4 1 0 3 -4 1

nomor 152x + 2y – 4z = -1 2 2 -4 -1 2 2 -4 -13y + 2z = 9 0 3 2 9 0 3 2 9-4x + y + 3z = 4,5 -4 1 3 4.5 0 5 -5 2.5

nomor 16-3x + 3y + 7z = 4 -3 3 7 4x – y + 2z = 3 1 -1 2 34x – 4y + z = 5 4 -4 1 5

nomor 173x – 12y = 6 3 -12 0 6-7x + 28y = -14 -7 28 0 -145x – 20y = 10 5 -20 0 10

nomor 182y – z = 1 0 2 -1 14x – 10y + 3z = 5 4 -10 3 53x – 3y = 6 3 -3 0 6

nomor 196x – 6y + 2z = 28 6 -6 2 28 -x + 9y – 3z = -10 -1 9 -3 -10 1/4x – y + 1/3z = 5/3 1/4 -1 1/3 1 2/3


0 0 -5.84615 -29.2308 0 0 -5.84615 -29.2308 0 0 -5.84615 -29.2308

2 2 -4 -1 2 0 -5.33333 -7 2 0 0 10 3 2 9 0 3 2 9 0 3 0 60 0 -8.33333 -12.5 0 0 -8.33333 -12.5 0 0 -8.33333 -12.5


0 0 1 5 x = 3

1 0 0 0.5 z = 1.50 1 0 2 y = 20 0 1 1.5 x = 0.5


nomor 203x + 4y + 6z = 1 3 4 6 1-2x + 8y – 4z = 2 -2 8 -4 24x – 8y + 8z = -2 4 -8 8 -2

nomor 215x + 3y = 22 5 3 0 22-4x + 7y = 20 -4 7 0 209x – 2y = 15 9 -2 0 15

nomor 224y + 7z = -13 0 4 7 -135x – 3y + 4z = - 23 5 -3 4 -23-x + 2y – 8z = 29 -1 2 -8 29pertukaran baris

5 -3 4 -23 5 -3 4 -23-1 2 -8 29 0 1.4 -7.2 24.40 4 7 -13 0 4 7 -13

nomor 236x + 18y – 4y = 20 6 18 -4 20-x – 3y + 8z = 4 -1 -3 8 45x + 5y – 9z = 11 5 5 -9 11

nomor 24w + x + y = 3 1 1 1 0 3 1 1 1 0 3-3w – 17x + y + 2z = 1 -3 -17 1 2 1 0 -14 4 2 104w – 17x + 8y – 5z = 1 4 -17 8 -5 1 0 -21 4 -5 -11-5x – 2y + z = 1 0 -5 -2 1 1 0 -5 -2 1 1


5 -3 4 -23 5 0 -11.4286 29.2857 5 0 0 -50 1.4 -7.2 24.4 0 1.4 -7.2 24.4 0 1.4 0 2.80 0 27.5714 -82.7143 0 0 27.5714 -82.7143 0 0 27.5714 -82.7143

1 1 1 0 3 1 1 1 0 3 1 0 1.28571 0.14286 3.714290 -14 4 2 10 0 -14 4 2 10 0 -14 4 2 100 0 -2 -8 -26 0 0 -2 -8 -26 0 0 -2 -8 -260 0 -3.42857 0.28571 -2.57143 0 0 0 14 42 0 0 0 14 42


1 0 0 -1 z = -30 1 0 2 y = 20 0 1 -3 x = -1

1 0 0 -5 -13 1 0 0 0 2 1 0 0 0 20 -14 0 -14 -42 0 -14 0 0 0 0 1 0 0 00 0 -2 -8 -26 0 0 -2 0 -2 0 0 1 0 10 0 0 14 42 0 0 0 14 42 0 0 0 1 3


nomor 25w – x + 3y – 3z = 3 1 -1 3 -3 3-5w + 2x – 5y + 4z =-5 -5 2 -5 4 -5-3w – 4x + 7y – 2z = 7 -3 -4 7 -2 72w + 3x + y – 11z = 1 2 3 1 -11 1

[ A ] { b }nomor 15-x - 3y + 8z = 4 -1 -3 8 46x + 18y - 4y = 20 6 18 -4 205x + 5y - 9z = 11 5 5 -9 11

Eliminasi ke-1 -1 -3 8 40 0 44 440 -10 31 31

Eliminasi ke-2 -1 -3 8 40 0 44 44

#DIV/0! ### ### ###

Eliminasi ke-3 #DIV/0! ### ### ####DIV/0! ### ### ####DIV/0! ### ### ###

Eliminasi ke-4 #DIV/0! ### ### ####DIV/0! ### ### ####DIV/0! ### ### ###

HASIL X Y Z#DIV/0! ### ### ####DIV/0! ### ### ####DIV/0! ### ### ###

[ A ] { b }nomor 224y + 7z = -13 5 -3 4 -235x – 3y + 4z = - 23 -1 2 -8 29-x + 2y – 8z = 29 0 4 7 -13

Eliminasi ke-1 5 -3 4 -230 1.4 -7.2 24.40 4 7 -13

Eliminasi ke-2 5 -3 4 -230 1.4 -7.2 24.40 0 27.571 -82.7143

Eliminasi ke-3 5 -3 0 -110 1.4 0 2.80 0 27.571 -82.7143

Eliminasi ke-4 5 0 0 -50 1.4 0 2.80 0 27.571 -82.7143

HASIL X Y Z1 0 0 -10 1 0 2

### ### 1 -3

nomor 15-x - 3y + 8z = 4 -1 -3 8 46x + 18y - 4y = 20 6 18 -4 205x + 5y - 9z = 11 5 5 -9 11

Eliminasi ke-1 -1 -3 8 40 0 44 440 -10 31 31

Eliminasi ke-2 -1 -3 8 40 -10 31 310 0 44 44

Eliminasi ke-3 -1 -3 0 -40 -10 0 00 0 44 44

Eliminasi ke-4 -1 0 0 -40 -10 0 00 0 44 44

HASIL X Y Z1 0 0 40 1 0 00 0 1 1

Documents

spl-gauss jordan.xlsx