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[?] Eliminate the variable X# on all the equations?

jose caballero
Posted 6 years ago

i want to eliminate all the x variables in all the systems but every time i try is not working: this is my code

equation1 = -318.1 x1 - 309.9 x2 + 993.1 x3 + 395.3 x4 - 599.2 x5 - 
   419.4 x6 + 676. x7 + 650.9 x8 + 512.9 x9 + 114.3 x10 - 491.7 x11 - 
   402.1 x12 + 111.4 x13 + 182.4 x14 - 593.9 x15 - 814.3 x16 + 
   91.7 x17 + 248.3 x18 - 421.3 x19 + 199.1 x20 - 711.4 x21 - 
   752.7 x22 == 249.7

equation2 = -281.9 x1 - 568.7 x2 + 206.9 x3 - 303.1 x4 + 674.3 x5 - 
   226.5 x6 + 507.4 x7 + 196.9 x8 + 764.6 x9 - 214.5 x10 - 
   587.5 x11 - 105.8 x12 - 869.8 x13 - 110.2 x14 + 431.9 x15 - 
   299.8 x16 + 979.4 x17 - 881.1 x18 - 16.6 x19 - 221.8 x20 - 
   33.5 x21 + 134.7 x22 == 637.8

equation3 = -577. x1 - 268.5 x2 - 692.2 x3 + 462.6 x4 + 81.4 x5 - 
   303.1 x6 + 736.6 x7 + 780.9 x8 + 560.8 x9 + 627.6 x10 + 
   698.8 x11 - 81.6 x12 + 436.9 x13 + 591.3 x14 + 651.7 x15 - 
   203.9 x16 + 449.1 x17 - 13.5 x18 + 964.6 x19 - 134.3 x20 + 
   692.6 x21 + 751.5 x22 == -462.

equation4 = -633.2 x1 - 500.6 x2 - 890.7 x3 + 10.4 x4 - 588. x5 + 
   144.1 x6 - 664.9 x7 + 777.8 x8 + 372. x9 + 684.1 x10 + 804.9 x11 - 
   215. x12 + 333.5 x13 - 860.5 x14 - 45.2 x15 - 10.3 x16 - 
   794.8 x17 + 992.3 x18 - 67.2 x19 - 200.6 x20 + 169.7 x21 + 
   70.6 x22 == 136.8

equation5 = -495.8 x1 + 823.8 x2 + 118.7 x3 - 219. x4 - 764. x5 + 
   785.8 x6 - 708.5 x7 + 224.4 x8 + 380.5 x9 - 517.9 x10 - 
   590.5 x11 - 967.3 x12 - 759. x13 - 981.3 x14 - 185.6 x15 - 
   703. x16 + 462.2 x17 + 793.8 x18 + 501.2 x19 + 11.8 x20 + 
   218.1 x21 - 727.9 x22 == -598.3

equation6 = 
 952.6 x1 - 555.6 x2 + 78.9 x3 + 601.1 x4 + 215.8 x5 - 255.1 x6 - 
   648.4 x7 + 576.4 x8 - 374.7 x9 - 253.8 x10 - 964.9 x11 + 
   576.1 x12 - 175.2 x13 - 71.6 x14 + 792. x15 + 118.1 x16 + 
   680.2 x17 - 632.4 x18 + 520.4 x19 - 789.7 x20 + 461.7 x21 - 
   141.9 x22 == 3.2

equation7 =
 -717.9 x1 - 333.2 x2 - 977.4 x3 - 270.4 x4 + 610.1 x5 - 736.9 x6 - 
   5.5 x7 + 955.7 x8 - 530.1 x9 + 416.5 x10 - 427.6 x11 - 424.8 x12 - 
   423.5 x13 - 670.7 x14 - 364.6 x15 - 422.1 x16 + 277.3 x17 + 
   118.1 x18 - 203.6 x19 - 793.4 x20 - 520.7 x21 + 828. x22 == 229.4

equation8 = -570.9 x1 - 209.9 x2 + 946.4 x3 + 906.4 x4 - 927.9 x5 + 
   779.3 x6 + 105.1 x7 + 438.7 x8 - 512. x9 - 788.2 x10 - 820.1 x11 - 
   951.3 x12 - 144.4 x13 - 219.8 x14 - 976. x15 + 955.4 x16 + 
   808.8 x17 + 375.8 x18 - 94.8 x19 + 111.2 x20 + 447.2 x21 - 
   102.6 x22 == 184.7

equation9 = 
 765.3 x1 - 780.6 x2 - 695.2 x3 - 656.6 x4 + 35.1 x5 - 853.9 x6 + 
   62.6 x7 - 194.2 x8 - 928.4 x9 - 939.1 x10 + 963.2 x11 - 
   460.8 x12 - 185.4 x13 + 223.1 x14 - 310.2 x15 - 61.4 x16 - 
   150.7 x17 - 232. x18 - 4.3 x19 + 497.3 x20 - 60.7 x21 + 684.8 x22 == 
  404.2

equation10 = -613.9 x1 + 606.2 x2 - 633.5 x3 + 578.5 x4 + 155.8 x5 + 
   397.8 x6 + 95.6 x7 - 327.6 x8 + 783.9 x9 - 677.1 x10 - 866.4 x11 + 
   839.8 x12 - 276.5 x13 + 457.1 x14 - 12.6 x15 + 765. x16 + 
   402.2 x17 - 539.8 x18 - 951.4 x19 + 741. x20 + 10.1 x21 - 
   21.3 x22 == 677.

equation11 = -974.4 x1 - 666.2 x2 + 706.6 x3 + 354.7 x4 - 416.6 x5 - 
   636.4 x6 - 443.9 x7 + 694.5 x8 + 450.9 x9 - 819.8 x10 - 
   891.7 x11 - 362.5 x12 + 874.9 x13 + 730.4 x14 + 516.2 x15 - 
   50.5 x16 + 559.3 x17 + 627.8 x18 + 8.9 x19 + 315.5 x20 + 
   70.5 x21 - 912.4 x22 == 617.1

equation12 = -908.1 x1 - 672. x2 + 731.1 x3 - 909.8 x4 - 413.6 x5 + 
   222.3 x6 + 272.4 x7 + 84.3 x8 + 137. x9 + 402.2 x10 + 812.6 x11 + 
   760.3 x12 + 785.5 x13 + 988.2 x14 + 31.1 x15 + 999. x16 - 
   544.8 x17 + 554.8 x18 + 647.5 x19 + 101.1 x20 - 969.4 x21 - 
   472.2 x22 == -106.5

equation13 = 
 395.5 x1 - 419.4 x2 - 278.8 x3 - 535.4 x4 + 211.9 x5 + 456.2 x6 - 
   637.8 x7 + 36.3 x8 - 542.7 x9 - 348.8 x10 + 113.8 x11 + 
   510.4 x12 - 701.2 x13 - 739.3 x14 + 192.8 x15 - 159.8 x16 + 
   452.8 x17 - 251.6 x18 + 945.3 x19 - 50.3 x20 + 339.5 x21 - 
   954.5 x22 == -459.5

equation14 = -233.4 x1 - 274.4 x2 + 784.3 x3 - 426.9 x4 + 441.4 x5 - 
   27. x6 - 552.6 x7 + 699.7 x8 + 869.7 x9 + 331.2 x10 - 646.9 x11 + 
   670.4 x12 + 993.3 x13 - 378.1 x14 - 648.3 x15 + 76. x16 - 
   364.8 x17 + 235.1 x18 - 337.3 x19 - 245.9 x20 - 21.4 x21 - 
   224.2 x22 == -448.5

equation15 = 
 608.8 x1 + 810.4 x2 + 943.2 x3 + 70.3 x4 + 113. x5 - 599. x6 - 
   726.2 x7 + 163.7 x8 - 303.6 x9 - 614.9 x10 + 459.5 x11 - 7.1 x12 + 
   131.3 x13 + 820.5 x14 + 556.5 x15 - 115.2 x16 - 404.8 x17 + 
   437.2 x18 - 34.1 x19 - 715.4 x20 - 187. x21 - 172. x22 == -222.6

equation16 = 
 601. x1 + 411.7 x2 - 606.8 x3 + 253.2 x4 - 463.5 x5 + 91.8 x6 + 
   294.6 x7 + 543.1 x8 - 466.2 x9 + 479.1 x10 + 428.4 x11 + 
   597.6 x12 - 631.5 x13 + 321.7 x14 - 868.7 x15 + 35.4 x16 + 
   727.9 x17 + 757.9 x18 + 300.3 x19 - 699.7 x20 + 381.2 x21 + 
   815.3 x22 == 38.4

equation17 = 
 463.2 x1 + 294. x2 - 28.1 x3 - 725.8 x4 - 735.1 x5 + 715.3 x6 - 
   80.1 x7 + 996.4 x8 - 814.8 x9 + 918.2 x10 + 703.6 x11 - 
   594.5 x12 - 892. x13 + 878.3 x14 + 373.9 x15 - 164.3 x16 - 
   598. x17 - 200.9 x18 - 527.9 x19 - 991.7 x20 + 762. x21 - 
   615.8 x22 == 986.9

equation18 = 
 753.2 x1 - 415.7 x2 - 327.8 x3 - 781.3 x4 - 391.6 x5 - 734.7 x6 + 
   473.1 x7 - 450.2 x8 + 343.4 x9 + 974.6 x10 + 92. x11 - 143.3 x12 + 
   272.2 x13 - 389.4 x14 + 189.6 x15 - 979.1 x16 + 196.3 x17 - 
   153.8 x18 + 913.7 x19 + 571.7 x20 - 420.1 x21 + 941.9 x22 == 189.5

equation19 = 
 84. x1 + 998.8 x2 + 96.7 x3 + 468.2 x4 - 711. x5 + 357.3 x6 - 
   501.4 x7 - 110.4 x8 - 478. x9 + 114.4 x10 + 69.3 x11 + 356.3 x12 + 
   9.5 x13 + 970.2 x14 + 425.5 x15 - 544.5 x16 - 844.8 x17 + 
   874.2 x18 - 102.2 x19 + 183.1 x20 + 588. x21 - 25.6 x22 == 936.1

equation20 = -675.2 x1 - 269.7 x2 - 829.9 x3 + 107.8 x4 - 908.1 x5 - 
   810.8 x6 - 664. x7 + 721.2 x8 - 173.7 x9 + 434.3 x10 + 518.8 x11 + 
   322.5 x12 + 719.3 x13 - 701.7 x14 + 29. x15 + 90.8 x16 - 
   47.7 x17 - 534.2 x18 + 419.6 x19 - 416.8 x20 + 303.3 x21 - 
   389.9 x22 == 378.8

equation21 = -351.7 x1 + 817.8 x2 - 373.1 x3 + 100.8 x4 - 605. x5 - 
   725.4 x6 - 162.2 x7 - 174.9 x8 - 191.2 x9 - 16. x10 - 796.3 x11 + 
   264.6 x12 + 839. x13 - 327.9 x14 + 130. x15 + 429.6 x16 + 
   108.2 x17 - 344.2 x18 + 374.3 x19 + 408.3 x20 - 268. x21 + 
   900.4 x22 == -444.8

equation22 = 
 345. x1 + 521.9 x2 + 746.8 x3 + 176.4 x4 + 960.2 x5 - 919.6 x6 - 
   311.7 x7 + 409.5 x8 - 809.9 x9 + 719.8 x10 - 55. x11 + 237.8 x12 - 
   168.2 x13 - 442.7 x14 - 677.7 x15 - 227.3 x16 - 296.4 x17 + 
   672.9 x18 + 574.1 x19 - 370.5 x20 + 413.9 x21 + 799. x22 == 352.

system = {equation1, equation2, equation3, equation4, equation5, 
   equation6, equation7, equation8, equation9, equation10, equation11,
    equation11, equation12, equation13, equation14, equation15, 
   equation16, equation17, equation18, equation19, equation20, 
   equation21, equation22};

TableForm[system];

m = 22;

n = 22;

mX = Array[StringJoin["x", ToString[#]] &, {n}]

TableForm@mSystem

MatrixForm@mB

Solve[system]
POSTED BY: jose caballero
6 Replies
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jose caballero
jose caballero
Posted 6 years ago

it worked to set up the x answers in a organize pattern from 1 to 22 but i need to set the 22 equations in a coefficient matrix form, do you have a way to eliminate the x on each equation and also set it up as a 22x22 matrix?
POSTED BY: jose caballero

OK, I see! Then try (using my definition of vars from above):

Coefficient[#, vars] &@*First /@ system

or likewise (using the new v11.3):

Curry[Coefficient][vars]@*First /@ system
POSTED BY: Henrik Schachner

Cool! Very nice use of the new Curry!
POSTED BY: Marco Thiel

Dear Marco,

glad you like my snippet of code! At the moment I am attending some boring conference, and your reply gives me the first sense of achievement for today ...

Best regard from Austria -- Henrik
POSTED BY: Henrik Schachner

Dear Henrik,

if that is so, you should obviously post more! I always like reading your posts. Your observations are always very astute and your solutions are elegant and beautiful. Your Computational Lichtenberg Figures are absolutely amazing.

Given your professional interest I still hope that you will show me a cool application of the RadonTransform! ;-)

All the best from Aberdeen and enjoy the remainder of your conference,

Marco
POSTED BY: Marco Thiel

How about:

x[n_] := ToExpression["x" <> ToString[n]]
vars = Array[x, 22];
Clear[x];
Solve[system, vars]
POSTED BY: Henrik Schachner
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