tugas numerik 5.6
DESCRIPTION
tugasTRANSCRIPT
10 -3 6 1 = 266 8 -2 2 = -122 0 -6 1 = -20
97 7 0 -9 = 79 Stambuk
Metode Cramer
Menghitung nilai h1
1 4 1 -2 1722 2 2 4
-5 3 3 14 4 2 -1
2 2 4
= -1 3 3 14 2 -1
= -1 2 2 3 1 - -2 3 1 + 4 3 32 -1 4 -1 4 2
= 1 2 x -5 - -2 x -7 + 4 x -6
= 1 -10 + 14 + -24
= -20
2 2 4
= -1 -5 3 14 2 -1
= -1 3 2 3 1 - -2 -5 1 + 4 -5 32 -1 4 -1 4 2
= -1 2 x -5 - -2 x 1 + 4 x -22
= -1 -10 - -2 + -88
= 100
X111+1
X121+2
2 2 4
= -1 -5 3 14 4 -1
= -1 4 2 3 1 - -2 -5 1 + 4 -5 34 -1 4 -1 4 4
= 1 2 x -7 - -2 x 1 + 4 x -32
= 1 -14 - -2 + -128
= -144
2 2 2
= -1 -5 3 34 4 2
= -1 4 2 3 3 - -2 -5 3 + 2 -5 34 2 4 2 4 4
= -1 2 x -6 - -2 x -22 + 2 x -32
= -1 -12 - 44 + -64
= 32
Det A 1 X11 + 4 X12 + 1 X13 + -2 X14= -20 + 400 + -144 + -64= 172
X131+3
X141+4
10 -3 6 1 = 26
6 8 -2 2 = -12
2 0 -6 1 = -20
97 7 0 -9 = 79 Stambuk
Metode Cramer
Menghitung nilai h1
CEK HASIL
26 -3 6 1 12550 Betul mhi
-12 8 -2 2
-20 0 -6 1
79 7 0 -9
h112550
= 0.672498 -2 2 18662
= -1 0 -6 1
7 0 -9
= -1 2 8 -6 1 - 2 0 1 + 2 0 -6
0 -9 7 -9 7 0
= 1 8 x 54 - 2 x -7 + 2 x 42
= 1 432 + -14 + 84
= 502
-12 -2 2
X111+1
= -1 -20 -6 1
79 0 -9
= -1 3 -12 -6 1 - 2 -20 1 + 2 -20 -6
0 -9 79 -9 79 0
= -1 -12 x 54 - 2 x 101 + 2 x 474
= -1 -648 - 202 + 948
= -502
-12 8 2
= -1 -20 0 1
79 7 -9
= -1 4 -12 0 1 - -8 -20 1 + 2 -20 0
7 -9 79 -9 79 7
= 1 -12 x -7 - -8 x 101 + 2 x -140
= 1 84 - -808 + -280
= -1004
-12 8 -2
= -1 -20 0 -6
79 7 0
= -1 4 -12 0 -6 - -8 -20 -6 + -2 -20 0
7 0 79 0 79 7
= -1 -12 x 42 - -8 x 474 + -2 x -140
X121+2
X131+3
X141+4
= -1 -504 - -3792 + 280
= 4016
Det h1 26 X11 + -3 X12 + 6 X13 + 1 X14
= 13052 + 1506 + -6024 + 4016
= 12550
Menghitung nilai h2
CEK HASIL
10 26 6 1 -12788 Betul mhi
6 -12 -2 2
2 -20 -6 1
97 79 0 -9
-12 -2 2h2
-12788= -0.68524
= -1 -20 -6 1 18662
79 0 -9
= -1 2 -12 -6 1 - 2 -20 1 + 2 -20 -6
0 -9 79 -9 79 0
= 1 -12 x 54 - 2 x 101 + 2 x 474
= 1 -648 + 202 + 948
= 502
6 -2 2
X111+1
= -1 2 -6 1
97 0 -9
= -1 3 6 -6 1 - 2 2 1 + 2 2 -6
0 -9 97 -9 97 0
= -1 6 x 54 - 2 x -115 + 2 x 582
= -1 324 - -230 + 1164
= -1258
6 -12 2
= -1 2 -20 1
97 79 -9
= -1 4 6 -20 1 - 12 2 1 + 2 2 -20
79 -9 97 -9 97 79
= 1 6 x 101 - 12 x -115 + 2 x 2098
= 1 606 - -1380 + 4196
= 3422
6 -12 -2
= -1 2 -20 -6
97 79 0
= -1 4 6 -20 -6 - 12 2 -6 + -2 2 -20
79 0 97 0 97 79
= -1 6 x 474 - 12 x 582 + -2 x 2098
X121+2
X131+3
X141+4
= -1 2844 - 6984 + -4196
= -5632
Det h2 10 X11 + 26 X12 + 6 X13 + 1 X14
= 5020 + -32708 + 20532 + -5632
= -12788
Menghitung nilai h3
CEK HASIL
10 -3 26 1 59974 Betul mhi
6 8 -12 2
2 0 -20 1
97 7 79 -9
8 -12 2h3
59974= 3.2137
= -1 0 -20 1 18662
7 79 -9
= -1 2 8 -20 1 - 12 0 1 + 2 0 -20
79 -9 7 -9 7 79
= 1 8 x 101 - 12 x -7 + 2 x 140
= 1 808 + -84 + 280
= 1004
6 -12 2
X111+1
= -1 2 -20 1
97 79 -9
= -1 3 6 -20 1 - 12 2 1 + 2 2 -20
79 -9 97 -9 97 79
= -1 6 x 101 - 12 x -115 + 2 x 2098
= -1 606 - -1380 + 4196
= -3422
6 8 2
= -1 2 0 1
97 7 -9
= -1 4 6 0 1 - -8 2 1 + 2 2 0
7 -9 97 -9 97 7
= 1 6 x -7 - -8 x -115 + 2 x 14
= 1 -42 - 920 + 28
= 906
6 8 -12
= -1 2 0 -20
97 7 79
= -1 4 6 0 -20 - -8 2 -20 + -12 2 0
7 79 97 79 97 7
= -1 6 x 140 - -8 x 2098 + -12 x 14
X121+2
X131+3
X141+4
= -1 840 - -16784 + -168
= 16112
Det h3 10 X11 + -3 X12 + 26 X13 + 1 X14
= 10040 + 10266 + 23556 + 16112
= 59974
Menghitung nilai h4
CEK HASIL
10 -3 6 26 -38496 Betul mhi
6 8 -2 -12
2 0 -6 -20
97 7 0 79
8 -2 -12h4
-38496= -2.0628
= -1 0 -6 -20 18662
7 0 79
= -1 2 8 -6 -20 - 2 0 -20 + -12 0 -6
0 79 7 79 7 0
= 1 8 x -474 - 2 x 140 + -12 x 42
= 1 -3792 + 280 + -504
= -4016
6 -2 -12
= -1 2 -6 -20
97 0 79
X111+1
X121+2
= -1 3 6 -6 -20 - 2 2 -20 + -12 2 -6
0 79 97 79 97 0
= -1 6 x -474 - 2 x 2098 + -12 x 582
= -1 -2844 - 4196 + -6984
= 5632
6 8 -12
= -1 2 0 -20
97 7 79
= -1 4 6 0 -20 - -8 2 -20 + -12 2 0
7 79 97 79 97 7
= 1 6 x 140 - -8 x 2098 + -12 x 14
= 1 840 - -16784 + -168
= -16112
6 8 -2
= -1 2 0 -6
97 7 0
= -1 4 6 0 -6 - -8 2 -6 + -2 2 0
7 0 97 0 97 7
= -1 6 x 42 - -8 x 582 + -2 x 14
= -1 252 - -4656 + -28
X131+3
X141+4
= 4432
Det h4 10 X11 + -3 X12 + 6 X13 + 26 X14
= -40160 + -16896 + -96672 + 115232
= -38496
Menghitung nilai h
CEK HASIL
10 -3 6 1 18662 Betul mhi
6 8 -2 2
2 0 -6 1
97 7 0 -9
8 -2 2
= -1 0 -6 1
7 0 -9
= -1 2 8 -6 1 - 2 0 1 + 2 0 -6
0 -9 7 -9 7 0
= 1 8 x 54 - 2 x -7 + 2 x 42
= 1 432 + -14 + 84
= 502
6 -2 2
= -1 2 -6 1
97 0 -9
= -1 3 6 -6 1 - 2 2 1 + 2 2 -6
X111+1
X121+2
0 -9 97 -9 97 0
= -1 6 x 54 - 2 x -115 + 2 x 582
= -1 324 - -230 + 1164
= -1258
6 8 2
= -1 2 0 1
97 7 -9
= -1 4 6 0 1 - -8 2 1 + 2 2 0
7 -9 97 -9 97 7
= 1 6 x -7 - -8 x -115 + 2 x 14
= 1 -42 - 920 + 28
= 906
6 8 -2
= -1 2 0 -6
97 7 0
= -1 4 6 0 -6 - -8 2 -6 + -2 2 0
7 0 97 0 97 7
= -1 6 x 42 - -8 x 582 + -2 x 14
= -1 252 - -4656 + -28
= 4432
X131+3
X141+4
Det A 10 X11 + -3 X12 + 6 X13 + 1 X14
= 5020 + 3774 + 5436 + 4432
= 18662
brs 1 10 -3 6 1 h1 = 26brs 2 6 8 -2 2 h2 = -12brs 3 2 0 -6 1 h3 = -20brs 4 97 7 0 -9 h4 = 79 Stambuk
pers 1 1 -0.3 0.6 0.1 h1 = 2.6 baris 1/ 10pers 2 6 -1.8 3.6 0.6 h2 = 15.6 pers. 1 * baris 2 elemen pivot 3pers 3 2 -0.6 1.2 0.2 h3 = 5.2 pers. 1 * baris 3 elemen pivot 2pers 4 97 -29.1 58.2 9.7 h4 = 252.2 pers. 1 * baris 4 elemen pivot 1
brs' 1 10 -3 6 1 h1 = 26brs' 2 0 9.8 -5.6 1.4 h2 = -27.6 brs 2 - pers 2brs' 3 0 0.6 -7.2 0.8 h3 = -25.2 brs 3 - pers 3brs' 4 0 36.1 -58.2 -18.7 h4 = -173.2 brs 4 - pers 4
pers 5 0 1 -0.571 0.143 = -2.8163 brs'2/ elemen pivotpers 6 0 0.6 -0.34 0.0857 = -1.6898 pers 5 x brs' 3pers 7 0 36.1 -20.63 5.1571 = -101.67 pers 5 x brs' 4
10 -3 6 1 = 26
0 9.8 -5.6 1.4 = -27.6brs" 3 0 0 -6.857 0.7143 = -23.51 brs'3 - pers 6brs" 4 0 0 -37.57 -23.9 = -71.531 brs'4 - pers 7
pers 8 0 0 1 -0.104 = 3.42857 brs" 3/ elemen pivotpers 9 0 0 -37.57 3.9137 = -128.82 pers 8 * baris" 4
h1 h2 h3 h4
10 -3 6 1 = 26.000 9.8 -5.6 1.4 = -27.600 0 -6.857 0.7143 = -23.510 0 0 -27.77 = 57.29 brs" 4 - pers 9
h4 = 57.29 = -2.0628-27.77
h3 = -23.51 - 0.71429 x -2.0628 = 3.2137-6.85714285714286
h2 = -27.60 - -5.6 x 3.2137 - 1.4 x -2.06 = -0.685249.8
h1 = 26.00 - -3 x -1 - 6 x 3.2 - 1 x -2.0628 = 0.6724910
10 -3 6 1 = 26 brs 16 8 -2 2 = -12 brs 22 0 -6 1 = -20 brs 3
97 7 0 -9 = 79 brs 4
1 -0.3 0.6 0.1 = 2.6 brs i brs 1/ -50 9.8 -5.6 1.4 = -27.6 brs 5 brs 2 - 3 x brs i0 0.6 -7.20 0.8 = -25.2 brs 6 brs 3 - 2 x brs i0 36.1 -58.20 -18.7 = -173.2 brs 7 brs 4 - 1 x brs i
1 -0.3 0.6 0.1 = 2.6 brs i0 1 -0.571 0.1429 = -2.816 brs ii brs 5 / (-2.8)0 0 -6.857 0.7143 = -23.51 brs 8 brs 6 - 0.8 x brs ii0 0 -37.57 -23.857 = -71.53 brs 9 brs 7 - 1.4 x brs ii
1 -0.3 0.6 0.1 = 2.6 baris i0 1 -0.571 0.1429 = -2.816 baris ii0 0 1 -0.1042 = 3.4286 brs iii brs 8 / -5.430 0 0 -27.771 = 57.286 brs 10 brs 9 - 1.5 x brs iii
1 -0.3 0.6 0.1 = 2.6 brs i0 1 -0.571 0.1429 = -2.816 brs ii0 0 1 -0.1042 = 3.4286 brs iii0 0 0 1 = -2.063 brs iv brs 10/5.51
1 -0.3 0.6 0 = 2.8063 brs i- (-0.2) x brs iv'0 1 -0.571 0 = -2.522 brs ii - (-0.57)x brs iv'0 0 1 0 = 3.2137 brs iii - (-0.34) x brs iv'0 0 0 1 = -2.063 brs iv'
1 -0.3 0 0 = 0.8781 brs i- (-0.2) x brs iii'0 1 0 0 = -0.685 brs ii- (-0.241)x brs iii'0 0 1 0 = 3.2137 brs iii'0 0 0 1 = -2.063 brs iv'
1 0 0 0 = 0.6725 brs i- (-0.4) x brs ii'0 1 0 0 = -0.685 brs ii'0 0 1 0 = 3.2137 brs iii'0 0 0 1 = -2.063 brs iv'
h1 h2 h3 h410 -3 6 1 = 26 brs 1
6 8 -2 2 = -12 brs 22 0 -6 1 = -20 brs 3
69 9 0 -6 = 96 brs 4
pers diatas dpt di tulis
h1 = 26 + 3 h2 - 6h3- h410
h2 = -12.0 - 6 h1 + 2h3 + 2h48
h3 = -20.0 - 2 h1 - h4-6
h4 = 96 - 69h1 - 9h2-6
Coba - Coba Masukan pers Coba - CobaIterasi h1 h2 h3 h4 h1 h2 h3 h4 Iterasi h1
0 2.6 -1.50 3.33 -16 4.1667 -0.475 1.533 -15.26 0 2.61 2.2 -2.00 3.83 -15.5 4.1667 -0.388 1.483 -15.33 1 1.752 1.8 -2.50 4.33 -15 4.1667 -0.3 1.433 -15.39 2 0.283 1.4 -3.00 4.83 -14.5 4.1667 -0.212 1.383 -15.46 3 1.534 1 -3.50 5.33 -14 4.1667 -0.125 1.333 -15.53 4 1.45 0.6 -4.00 5.83 -13.5 4.1667 -0.038 1.283 -15.59 5 0.326 0.2 -4.50 6.33 -13 4.1667 0.05 1.233 -15.66 6 1.667 -0.2 -5.00 6.83 -12.5 4.1667 0.137 1.183 -15.73 7 1.168 -0.6 -5.50 7.33 -12 4.1667 0.225 1.133 -15.79 8 0.469 -1 -6.00 7.83 -11.5 4.1667 0.313 1.083 -15.86 9 1.7310 -1.4 -6.50 8.33 -11 4.1667 0.4 1.033 -15.93 10 0.9511 -1.8 -7.00 8.83 -10.5 4.1667 0.488 0.983 -16 11 0.6312 -2.2 -7.50 9.33 -10 4.1667 0.575 0.933 -16.06 12 1.7413 -2.6 -8.00 9.83 -9.5 4.1667 0.663 0.883 -16.13 13 0.7814 -3 -8.50 10.3 -9 4.1667 0.75 0.833 -16.19 14 0.81
h1 1.68h2 -5h3 1.42h4 -4.15
Coba - Coba Masukan persh2 h3 h4 h1 h2 h3 h4 h1 h2 h3 h4
-1.50 3.33 -16 1.75 -6.617 1.5333 -5.8 -48.57% 77.33% -117.39% -175.86%-6.62 1.53 -5.8 0.275 -3.879 2.95 -18.656 -536.36% -70.57% 48.02% 68.91%-3.88 2.95 -18.66 1.5319 -5.633 0.3156 -6.8327 82.05% 31.13% -834.65% -173.05%-5.63 0.32 -6.833 1.404 -4.278 2.7052 -6.2707 -9.10% -31.66% 88.33% -8.96%-4.28 2.71 -6.271 0.3205 -3.444 2.7562 -17.481 -338.06% -24.21% 1.85% 64.13%-3.44 2.76 -17.48 1.661 -5.422 0.5267 -5.0307 80.70% 36.47% -423.29% -247.48%-5.42 0.53 -5.031 1.1606 -3.872 3.0486 -8.4609 -43.12% -40.03% 82.72% 40.54%-3.87 3.05 -8.461 0.4554 -3.724 2.31 -16.348 -154.83% -3.98% -31.97% 48.24%-3.72 2.31 -16.35 1.7317 -5.351 0.7605 -4.112 73.70% 30.41% -203.75% -297.57%-5.35 0.76 -4.112 0.9496 -3.637 3.2252 -10.535 -82.36% -47.14% 76.42% 60.97%-3.64 3.23 -10.53 0.6273 -4.04 1.8941 -14.845 -51.37% 9.97% -70.28% 29.04%
-4 1.89 -14.84 1.7362 -5.208 1.0683 -3.8462 63.87% 22.44% -77.30% -285.96%-5.21 1.07 -3.846 0.7812 -3.497 3.271 -12.261 -122.25% -48.95% 67.34% 68.63%-3.5 3.27 -12.26 0.8145 -4.333 1.5502 -13.133 4.09% 19.31% -111.01% 6.64%-4.33 1.55 -13.13 1.6832 -5.007 1.416 -4.1535 51.61% 13.45% -9.48% -216.19%
ea
h1 h2 h3 h4-5 2 1 1 = -14.7 brs 13 -4 0 1 = -16.3 brs 22 0 -6 1 = -15.8 brs 31 1 1 4 = -16.7 brs 4
pers diatas dpt di tulis
h1 = -14.7 - 2 h2 - h3 - h4-5
h2 = -16.3 - 3 h1 - h4-4
h3 = -15.8 - 2 h1 - h4-6
h4 = -16.7 - h1 - h2 - h34
Coba - Coba Masukan pers Coba - CobaIterasi h1 h2 h3 h4 h1 h2 h3 h4 Iterasi h1
0 2.94 6.28 3.61 -7.38 4.698 5.753 2.969 -7.53 0 2.941 4.698 7.599 4.199 -8.299 1 4.72 2 4.333 3 4.224 4 4.215 5 4.216 6 4.217 7 4.218 8 4.219 9 4.2110 10 4.2111 11 4.2112 12 4.2113 13 4.2114 14 4.21
h1 4.21h2 5.41h3 2.82h4 -7.29
Coba - Coba Masukan persh2 h3 h4 h1 h2 h3 h4 h1 h2 h3 h4
6.28 3.61 -7.383 4.698 5.753 2.9688 -7.5299 37.42% -9.17% -21.71% 1.95%5.75 2.97 -7.53 4.3289 5.439 2.8213 -7.3223 -8.53% -5.76% -5.23% -2.83%5.44 2.82 -7.322 4.2155 5.406 2.8181 -7.2849 -2.69% -0.61% -0.11% -0.51%5.41 2.82 -7.285 4.209 5.411 2.8222 -7.2855 -0.15% 0.08% 0.15% 0.01%5.41 2.82 -7.285 4.2116 5.412 2.8229 -7.2867 0.06% 0.03% 0.03% 0.02%5.41 2.82 -7.287 4.2122 5.412 2.8229 -7.2869 0.01% 0.00% 0.00% 0.00%5.41 2.82 -7.287 4.2122 5.412 2.8229 -7.2869 0.00% 0.00% 0.00% 0.00%5.41 2.82 -7.287 4.2122 5.412 2.8229 -7.2869 0.00% 0.00% 0.00% 0.00%5.41 2.82 -7.287 4.2122 5.412 2.8229 -7.2869 0.00% 0.00% 0.00% 0.00%5.41 2.82 -7.287 4.2122 5.412 2.8229 -7.2869 0.00% 0.00% 0.00% 0.00%5.41 2.82 -7.287 4.2122 5.412 2.8229 -7.2869 0.00% 0.00% 0.00% 0.00%5.41 2.82 -7.287 4.2122 5.412 2.8229 -7.2869 0.00% 0.00% 0.00% 0.00%5.41 2.82 -7.287 4.2122 5.412 2.8229 -7.2869 0.00% 0.00% 0.00% 0.00%5.41 2.82 -7.287 4.2122 5.412 2.8229 -7.2869 0.00% 0.00% 0.00% 0.00%5.41 2.82 -7.287 4.2122 5.412 2.8229 -7.2869 0.00% 0.00% 0.00% 0.00%
ea
