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Module 5: Doing Math
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266 lines (257 loc) · 15.1 KB
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> # Set the values for A and B
> A = matrix(1:100, nrow=10)
> B <- matrix(1:1000, nrow=10)
> # Create the seed so we can have the same outputted matrix for A and B
> set.seed(123)
> # The matrix will run by using the runif function
> A <- matrix(runif(100, min=1, max=100), nrow=10)
> #Output matrix A
> A
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 29.470174 95.726501 89.06439 96.339399 15.13720 5.537286 66.84640
[2,] 79.042208 45.880081 69.58754 90.327605 42.04009 44.777807 10.38923
[3,] 41.488715 68.079493 64.41017 69.379823 41.95871 80.093560 39.01299
[4,] 88.418723 57.690707 99.43271 79.751274 37.51570 13.068027 28.16398
[5,] 94.106261 11.189544 65.91487 3.436755 16.09203 56.533850 81.64936
[6,] 5.510093 90.082672 71.14452 48.301801 14.74180 21.446608 45.40312
[7,] 53.282443 25.362686 54.86254 76.087494 24.07038 13.625633 81.19637
[8,] 89.349485 5.163894 59.82006 22.424386 47.13028 75.577479 81.42656
[9,] 55.592066 33.464151 29.62681 32.499920 27.33129 89.609491 79.63989
[10,] 46.204859 95.495861 15.56425 23.930953 85.92494 38.071815 44.54334
[,8] [,9] [,10]
[1,] 75.693041 25.11833 13.93887
[2,] 63.292892 67.13750 65.65709
[3,] 71.308058 42.34703 35.00813
[4,] 1.061853 79.03139 66.01905
[5,] 48.056341 11.18360 32.71695
[6,] 22.791770 44.05438 19.58142
[7,] 38.601837 98.51074 78.44714
[8,] 61.664329 89.41206 10.26590
[9,] 35.827993 88.76044 47.21113
[10,] 12.002407 18.33021 51.63904
> # Set runif function for matrix B now
> B <- matrix(runif(1000, min=1, max=1000), nrow=10)
> #Output matrix B
> B
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 600.3890 935.36450 648.24559 619.6372 312.39050 847.6057 502.7973
[2,] 333.4907 301.92767 320.50080 891.5027 410.06548 498.0297 354.5507
[3,] 489.1244 61.65985 308.41229 673.3261 11.45664 388.5211 650.3352
[4,] 954.5194 947.77921 220.54786 737.3407 184.66567 247.2025 375.3392
[5,] 483.4195 720.87568 370.11938 521.6146 842.88659 111.9854 356.0899
[6,] 890.4599 143.15200 984.23498 660.1786 231.93062 390.6044 534.1543
[7,] 914.5237 549.73537 155.04810 821.9837 239.86086 572.3634 740.5940
[8,] 609.1262 954.13715 91.95296 786.4953 77.61447 217.6759 221.8818
[9,] 411.2791 585.89787 142.76500 979.8421 246.47795 445.3232 413.3334
[10,] 147.9476 405.10577 690.31709 439.9921 732.40307 218.7727 266.4210
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 630.3431 839.9280 274.8925 239.4873 482.56056 283.2458 618.73288
[2,] 184.6447 313.1357 322.1613 962.3966 253.71196 961.1437 428.99309
[3,] 863.7805 708.5820 985.6552 601.7644 217.03853 728.6660 542.53829
[4,] 746.8214 265.7528 620.3733 515.5147 674.70201 686.6887 59.42001
[5,] 668.6164 594.7489 937.3768 403.1708 48.61596 53.7911 261.59600
[6,] 618.3999 481.8085 467.0662 880.3663 701.15223 395.8249 397.75480
[7,] 372.8658 265.7677 407.4258 364.7278 352.53675 478.3675 198.54699
[8,] 530.3059 565.0258 659.5711 288.9510 409.53505 560.6930 832.09564
[9,] 874.8077 913.2750 153.1943 171.4746 821.13037 698.5633 153.73434
[10,] 582.1683 901.9725 573.2942 172.9996 918.93849 915.7679 803.61512
[,15] [,16] [,17] [,18] [,19] [,20]
[1,] 547.2793 257.9595 925.78225 871.172370 758.83458 298.44404
[2,] 662.6553 222.5661 882.09558 7.294483 137.96897 101.62086
[3,] 172.5268 593.4526 674.51266 72.985067 397.18801 72.83219
[4,] 633.4223 268.2539 950.21681 165.047014 225.76034 880.56013
[5,] 312.5579 531.5393 516.92845 770.563740 58.90060 754.49315
[6,] 724.8298 785.5064 576.94250 735.449122 396.49680 816.78928
[7,] 399.5409 168.8927 336.99487 971.903760 65.86337 982.15823
[8,] 969.3871 404.9948 347.97731 467.005904 226.66055 104.49605
[9,] 967.4310 472.1047 21.00428 75.310129 55.57448 99.94279
[10,] 726.9758 868.2387 503.31023 649.169306 670.61176 799.03278
[,21] [,22] [,23] [,24] [,25] [,26]
[1,] 784.790691 390.19752 853.90961 617.6180 415.3206 137.4037
[2,] 10.420475 465.20128 296.59956 286.9991 120.2854 967.5020
[3,] 779.286817 713.56572 147.90128 738.0596 526.5036 515.5567
[4,] 729.661261 56.24662 704.28807 834.2203 225.8483 163.9073
[5,] 630.501721 355.42831 104.70288 314.9565 486.9254 622.2804
[6,] 481.429919 803.00946 34.69405 493.0740 370.8446 985.9682
[7,] 157.480215 835.87313 999.40512 697.6764 983.3668 669.1027
[8,] 9.207304 238.51166 35.83993 641.8209 388.9308 419.4970
[9,] 453.005936 354.63212 339.05289 644.2790 230.0156 324.0216
[10,] 492.801035 857.02853 915.14870 977.8756 623.6742 835.4201
[,27] [,28] [,29] [,30] [,31] [,32] [,33]
[1,] 144.67323 422.4231 585.31519 977.1219 986.06824 317.63230 547.9120
[2,] 193.62313 343.4660 761.06280 297.0059 137.93040 831.73703 644.5960
[3,] 896.84194 866.6168 373.33669 726.2570 905.40427 215.95691 596.6673
[4,] 308.81143 455.6529 769.42472 785.9021 576.72554 498.45099 322.6154
[5,] 363.93724 534.2311 538.13951 106.3123 396.05341 276.77362 891.2232
[6,] 784.16253 963.8795 914.08145 240.3550 450.35268 192.83130 626.6307
[7,] 194.18530 774.8170 186.11115 271.2743 706.79540 950.67064 303.6020
[8,] 18.74805 209.6675 282.93620 101.9574 83.42024 322.40381 388.8165
[9,] 407.20126 309.4780 95.86745 118.7959 339.97327 478.97793 161.3146
[10,] 483.68450 971.3711 211.27659 991.2453 681.10676 28.96458 862.6893
[,34] [,35] [,36] [,37] [,38] [,39] [,40]
[1,] 953.1481 283.7099 524.2988 974.7511 94.822690 215.9513 971.46663
[2,] 564.0810 584.2885 350.4520 436.6939 822.208041 814.1198 71.41849
[3,] 330.2179 731.9760 241.2902 464.5526 428.000852 308.4561 460.32541
[4,] 996.6206 166.3554 59.1336 166.1328 756.131372 688.0549 701.88353
[5,] 235.5849 866.6013 237.3831 585.3516 662.723121 932.7484 87.85323
[6,] 613.0593 708.8656 890.1878 271.5072 445.082870 116.6639 992.95107
[7,] 109.0704 760.6391 812.0156 230.8668 627.519038 128.5780 253.84590
[8,] 487.5455 147.9370 747.7688 691.5166 1.464884 678.5456 50.48890
[9,] 100.3464 358.6989 155.7568 283.5695 218.026271 429.5196 686.63862
[10,] 162.0046 673.6591 125.6173 810.5877 705.167373 834.5666 787.14043
[,41] [,42] [,43] [,44] [,45] [,46]
[1,] 354.25247 465.24906 301.84138 939.1993 801.14726 328.26980
[2,] 367.07500 83.44865 365.30636 687.9200 92.55305 205.73376
[3,] 287.81303 860.24674 312.80068 447.5900 832.27567 569.81328
[4,] 80.89294 396.26498 38.33259 816.6617 277.57822 888.16714
[5,] 366.08882 736.16345 519.28612 40.4597 753.35699 530.18438
[6,] 178.83580 172.57166 679.33440 739.2927 964.18842 587.37170
[7,] 536.51767 455.30687 903.33033 349.3708 82.38509 666.06941
[8,] 504.44476 770.43455 26.50117 829.4216 854.51038 530.36257
[9,] 945.09007 63.58735 989.08919 536.0059 802.43598 510.33306
[10,] 341.97996 815.26641 303.58474 275.2708 385.78843 17.14432
[,47] [,48] [,49] [,50] [,51] [,52]
[1,] 48.66227 553.76067 878.7953 527.06349 237.9925 630.11568
[2,] 929.42133 906.14206 813.0398 61.72144 686.8039 97.53711
[3,] 769.51625 587.87391 854.2459 969.06982 226.5926 22.97172
[4,] 201.87954 424.04019 368.5281 121.11689 319.1761 993.05174
[5,] 650.61124 949.63574 874.0760 89.27494 174.8098 584.35491
[6,] 654.11292 709.32887 152.1868 880.88335 801.6282 782.04124
[7,] 395.85851 413.89210 282.5299 508.86226 147.1358 892.00423
[8,] 812.49252 19.34572 667.0385 338.15750 822.8947 755.11059
[9,] 547.47639 567.16735 977.4062 894.44029 331.6668 979.22453
[10,] 885.24752 490.57339 583.1570 32.93966 374.7952 45.10292
[,53] [,54] [,55] [,56] [,57] [,58]
[1,] 903.49748 759.3762 594.24465 753.17913 845.71057 21.05394
[2,] 865.63531 844.9898 799.02473 917.14008 806.62873 521.79253
[3,] 775.63218 458.4636 888.52024 476.27476 118.21390 87.19162
[4,] 377.43960 729.9020 385.80640 567.55235 712.97387 283.71934
[5,] 43.06594 104.9746 91.23176 736.88373 236.03359 421.01447
[6,] 365.04667 220.7632 626.11789 857.58998 75.88179 587.69085
[7,] 274.47752 953.9973 745.89058 909.23736 935.71050 806.88774
[8,] 850.61701 752.2855 86.29308 57.32584 158.01066 202.79321
[9,] 363.03931 819.1364 301.21709 503.40540 647.41029 459.96525
[10,] 305.17331 418.3593 614.94760 351.19423 174.34423 448.69497
[,59] [,60] [,61] [,62] [,63] [,64]
[1,] 734.0140 40.74086 845.08861 631.142825 419.25049 417.497635
[2,] 715.0401 635.16571 260.87234 521.321509 718.16666 875.007505
[3,] 831.3908 540.02135 24.12135 659.961716 742.79659 647.699669
[4,] 886.6796 140.96345 862.53714 729.631570 872.12682 924.554508
[5,] 952.6919 284.42807 335.25337 487.336050 608.26009 173.052871
[6,] 551.0661 583.44756 632.15708 385.072159 756.44715 316.496976
[7,] 522.8134 165.86087 546.87983 7.826675 847.39406 804.452023
[8,] 171.5276 97.20481 377.06805 4.680543 613.16687 988.974448
[9,] 479.7923 429.18448 186.68714 994.941504 793.43094 323.063166
[10,] 254.5670 356.40580 429.51165 108.778993 23.83183 2.190437
[,65] [,66] [,67] [,68] [,69] [,70] [,71]
[1,] 992.17845 278.49155 514.2674 916.0703 259.54240 933.7628 471.21115
[2,] 149.20404 250.15718 237.1035 813.3000 819.64767 542.9891 366.47963
[3,] 50.31493 160.27604 575.8602 676.2141 16.46219 220.2031 122.15078
[4,] 597.75613 72.55843 482.7757 807.6916 654.74637 489.9384 47.94669
[5,] 322.00712 557.88015 569.7833 128.9364 811.90786 801.3476 263.53351
[6,] 528.40107 490.34721 145.0082 251.5278 461.90756 408.2230 968.67253
[7,] 795.62660 494.79807 146.5631 332.2154 204.21368 104.6079 489.00699
[8,] 69.86366 888.48321 412.8708 407.8620 19.74945 281.2846 478.34421
[9,] 695.32568 37.66766 683.3273 635.7322 283.84956 362.1048 749.04409
[10,] 948.68288 204.54007 653.7744 808.8034 915.35735 259.9856 667.97259
[,72] [,73] [,74] [,75] [,76] [,77]
[1,] 50.36618 689.03240 5.102834 962.45890 326.90691 425.02764
[2,] 695.41014 311.95954 772.137573 736.59770 726.67249 43.31832
[3,] 363.89831 605.98125 463.512236 613.11075 991.75349 647.79470
[4,] 884.24947 991.04328 721.119510 120.80895 715.41839 469.15054
[5,] 775.52193 743.46171 666.839211 550.70879 504.93537 618.30820
[6,] 140.06444 76.78127 572.501647 263.49352 436.61162 271.54462
[7,] 295.71426 451.71774 704.109137 898.46247 948.87643 158.13799
[8,] 126.95670 54.48340 657.563839 10.17077 121.06131 115.14002
[9,] 590.31172 340.21596 290.062793 236.99870 76.07003 508.17518
[10,] 562.11393 734.21820 98.142216 130.91455 889.13247 548.48426
[,78] [,79] [,80] [,81] [,82] [,83]
[1,] 141.50554 108.1874 566.08869 923.77551 4.892447 808.57787
[2,] 170.59928 921.1441 756.89348 543.05577 53.146417 42.87758
[3,] 762.22334 675.6870 669.93394 852.51224 866.693620 364.37895
[4,] 527.86755 149.4451 546.97627 583.97930 576.668924 856.74037
[5,] 861.12837 745.5965 811.65219 668.65532 314.528729 698.24863
[6,] 673.88143 942.6563 759.40764 511.80328 959.506318 684.80199
[7,] 14.02799 421.3626 21.04840 762.98784 591.602563 348.66704
[8,] 693.50570 298.4254 381.52280 903.45893 531.877926 555.12715
[9,] 891.82202 260.1672 51.82923 820.65404 384.552735 138.10637
[10,] 632.21833 223.6584 798.10503 72.36042 320.233676 785.14662
[,84] [,85] [,86] [,87] [,88] [,89]
[1,] 886.97571 975.91380 560.72026 508.6499 782.186946 458.4189
[2,] 204.89179 490.73397 156.71828 450.1503 46.980522 711.9809
[3,] 770.85234 389.78115 956.62318 623.6381 820.024823 919.9282
[4,] 596.76660 418.13740 44.92266 140.8380 270.139039 627.4836
[5,] 957.71207 93.83289 372.78558 908.0385 283.567564 902.2796
[6,] 159.52971 162.64740 962.65273 569.8738 643.578338 757.5718
[7,] 526.44830 406.01108 645.78209 548.7323 948.170719 138.7205
[8,] 873.27822 342.47263 62.20135 117.7108 7.991456 154.1016
[9,] 869.83636 415.84220 410.53598 762.2663 352.266054 192.1209
[10,] 24.66495 304.74842 426.47923 478.8911 419.626679 433.7520
[,90] [,91] [,92] [,93] [,94] [,95] [,96]
[1,] 88.13208 274.34911 462.63676 461.7554 231.9997 833.46148 709.1465
[2,] 224.55622 594.27307 341.59344 792.9456 543.6897 719.86770 826.8888
[3,] 572.57653 161.02463 185.95518 585.9800 448.1226 457.42987 892.0044
[4,] 400.76901 853.57681 507.49073 395.3642 131.1578 521.74300 539.8713
[5,] 565.89992 847.89142 20.17184 811.4261 622.1043 243.21462 555.7583
[6,] 829.79425 478.40893 773.91235 319.2445 548.4463 76.78497 277.1634
[7,] 642.47171 773.91843 560.10541 581.8659 150.0950 391.90380 659.5387
[8,] 392.10725 296.10468 641.82118 456.0335 559.9863 14.09511 244.1918
[9,] 709.87027 66.56248 468.96369 269.5346 427.4587 867.63197 288.9779
[10,] 109.71525 441.09259 279.94459 555.6220 448.2824 992.62306 716.0652
[,97] [,98] [,99] [,100]
[1,] 727.80610 788.62097 392.93892 806.44169
[2,] 173.87000 849.06517 172.76490 79.92668
[3,] 307.00495 878.16373 320.32248 116.22207
[4,] 370.53737 800.67590 414.14151 130.28687
[5,] 78.64383 640.50834 759.57636 739.00979
[6,] 713.43704 629.29883 272.61831 757.34143
[7,] 551.37181 272.13760 116.46687 992.46285
[8,] 136.72953 30.90989 30.30728 624.92843
[9,] 974.18953 420.44435 807.04844 289.40142
[10,] 562.40120 356.07924 480.64631 200.71186
> # Solve for the matrix A inverse
> solve(A)
[,1] [,2] [,3] [,4] [,5]
[1,] 0.012404331 0.014655568 -0.024950989 0.002363324 0.0024883203
[2,] 0.005498005 0.018905283 -0.025300934 -0.008300409 0.0010619645
[3,] -0.013711628 -0.010417761 0.019364467 0.004667232 0.0055394390
[4,] 0.016471142 -0.022182260 0.020340061 0.019413907 -0.0105374733
[5,] -0.007553095 -0.017673061 0.024248454 0.005571115 -0.0059687886
[6,] -0.002072423 -0.011888989 0.018786337 0.007942099 -0.0007145655
[7,] 0.006674229 -0.018906014 0.008345737 0.005219274 0.0007914594
[8,] -0.003758705 0.025465328 -0.015070004 -0.022802631 0.0051107692
[9,] -0.003791975 0.014823496 -0.017791253 -0.007537918 -0.0051919999
[10,] -0.014208379 0.008644982 0.002271745 -0.008820289 0.0094544005
[,6] [,7] [,8] [,9]
[1,] -0.007528454 -0.0155334345 -0.0006610557 0.016073655
[2,] 0.014340780 -0.0126398624 -0.0031970118 0.012703786
[3,] 0.012004889 0.0086199292 0.0039862656 -0.020829129
[4,] -0.033021567 -0.0004251472 -0.0056725764 0.009574390
[5,] -0.008097359 0.0116419862 0.0105975716 -0.021416142
[6,] -0.008617087 -0.0040702093 -0.0047360911 0.007951269
[7,] -0.011320821 0.0069961331 -0.0008031338 0.002070228
[8,] 0.017684411 0.0024590013 0.0049765108 -0.008003417
[9,] 0.015235601 -0.0016023448 0.0075767455 0.003805645
[10,] 0.011974071 0.0124641286 -0.0093644472 -0.007537431
[,10]
[1,] 0.0022233330
[2,] 0.0043549557
[3,] -0.0050540560
[4,] -0.0026334849
[5,] 0.0075871860
[6,] -0.0036383211
[7,] 0.0013363260
[8,] 0.0006537543
[9,] -0.0011647558
[10,] 0.0012324687
> Output the determinant for A
> det(A)
[1] 2.471786e+18
> Solve for the matrix B inverse
> solve(B)
Error in solve.default(B) : 'a' (10 x 100) must be square
> # The B matrix was not square and the inverse could not be solved
> det(B)
Error in determinant.matrix(x, logarithm = TRUE, ...) :
'x' must be a square matrix
> # Since the B matrix could not be solved for its inverse, we also could not receive its determinant