p=5; sqrtsq([0 .1 .5 .9 1 1.5 2], p) ans = Columns 1 through 4 0 0.100000000000000 0.500000000000000 0.900000000000000 Columns 5 through 7 1.000000000000000 1.500000000000000 2.000000000000000 p=5; sqsqrt([0 .1 .5 .9 1 1.5 2], p) ans = Columns 1 through 4 0 0.100000000000000 0.499999999999999 0.900000000000002 Columns 5 through 7 1.000000000000000 1.499999999999997 1.999999999999996 clc p=5; sqsqrt([0 .1 .5 .9 1 1.5 2], p) ans = Columns 1 through 4 0 0.100000000000000 0.499999999999999 0.900000000000002 Columns 5 through 7 1.000000000000000 1.499999999999997 1.999999999999996 p=5; sqsqrt([0 .1 .5 .9 1 1.5 2], p) ans = Columns 1 through 4 0 0.100000000000000 0.499999999999999 0.900000000000002 Columns 5 through 7 1.000000000000000 1.499999999999997 1.999999999999996 clc diary off p=5; sqsqrt([0 .1 .5 .9 1 1.5 2], p) ans = Columns 1 through 4 0 0.100000000000000 0.499999999999999 0.900000000000002 Columns 5 through 7 1.000000000000000 1.499999999999997 1.999999999999996 p=5; sqrtsq([0 .1 .5 .9 1 1.5 2], p) ans = Columns 1 through 4 0 0.100000000000000 0.500000000000000 0.900000000000000 Columns 5 through 7 1.000000000000000 1.500000000000000 2.000000000000000 p=5; sqsqrt([.1 .5 .9 1.5 2], p) ans = Columns 1 through 4 0.100000000000000 0.499999999999999 0.900000000000002 1.499999999999997 Column 5 1.999999999999996 p=5; sqsqrt([.1 .9 1.5 2], p) ans = 0.100000000000000 0.900000000000002 1.499999999999997 1.999999999999996 p=5; sqrtsq([.1 .9 1.5 2], p) ans = 0.100000000000000 0.900000000000000 1.500000000000000 2.000000000000000 p=10; sqrtsq([.1 .9 1.5 2], p) ans = 0 0.900000000000000 1.500000000000000 Inf p=7; sqrtsq([.1 .9 1.5 2], p) ans = 0.100000000000000 0.900000000000000 1.500000000000000 2.000000000000000 p=8; sqrtsq([.1 .9 1.5 2], p) ans = 0.100000000000000 0.900000000000000 1.500000000000000 2.000000000000000 p=9; sqrtsq([.1 .9 1.5 2], p) ans = 0 0.900000000000000 1.500000000000000 2.000000000000000 .1^2 ans = 0.010000000000000 .1^2^2 ans = 1.000000000000000e-04 .1^2^2^2 ans = 1.000000000000001e-08 2^-2050 ans = 0 2^-1050 ans = 8.289046058458095e-317 2^-1070 ans = 7.905050333459945e-323 2^-1072 ans = 1.976262583364986e-323 2^-1075 ans = 0 2^-1074 ans = 4.940656458412465e-324 p=9; sqrtsq([.1 .9 1.5 2], p) ans = 0 0.900000000000000 1.500000000000000 2.000000000000000 p=8; sqrtsq([.1 .9 1.5 2], p) ans = 0.100000000000000 0.900000000000000 1.500000000000000 2.000000000000000 p=8; sqrtsq([.5 .9 1.5 2], p) ans = 0.500000000000000 0.900000000000000 1.500000000000000 2.000000000000000 p=9; sqrtsq([.5 .9 1.5 2], p) ans = 0.500000000000000 0.900000000000000 1.500000000000000 2.000000000000000 p=10; sqrtsq([.5 .9 1.5 2], p) ans = 0.500000000000000 0.900000000000000 1.500000000000000 Inf p=11; sqrtsq([.5 .9 1.5 2], p) ans = 0 0.900000000000000 Inf Inf .5^2 ans = 0.250000000000000 .5^2^2 ans = 0.062500000000000 p=11; sqrtsq([.5 .9 1.5 2], p) ans = 0 0.900000000000000 Inf Inf p=13; sqrtsq([.5 .9 1.5 2], p) ans = 0 0 Inf Inf p=12; sqrtsq([.5 .9 1.5 2], p) ans = 0 0.900000000000000 Inf Inf p=8; sqrtsq([.5 .9 1.5 2], p) ans = 0.500000000000000 0.900000000000000 1.500000000000000 2.000000000000000 p=8; sqrtsq([1.1 1.5 2], p) ans = 1.100000000000000 1.500000000000000 2.000000000000000 p=9; sqrtsq([1.1 1.5 2], p) ans = 1.100000000000000 1.500000000000000 2.000000000000000 p=10; sqrtsq([1.1 1.5 2], p) ans = 1.100000000000000 1.500000000000000 Inf 1/0 ans = Inf Inf/0 ans = Inf Inf/Inf ans = NaN 2^1020 ans = 1.123558209288947e+307 2^1030 ans = Inf 2^1024 ans = Inf 2^1022 ans = 4.494232837155790e+307 2^1023 ans = 8.988465674311580e+307 2^2^2^2 ans = 256 2^2^2^2^2 ans = 65536 2^1024 ans = Inf p=10; sqrtsq([1.1 1.5 2], p) ans = 1.100000000000000 1.500000000000000 Inf p=9; sqrtsq([1.1 1.5 2], p) ans = 1.100000000000000 1.500000000000000 2.000000000000000 p=11; sqrtsq([1.1 1.5 2], p) ans = 1.100000000000000 Inf Inf 1.1^2 ans = 1.210000000000000 1.1^2^2 ans = 1.464100000000000 1.1^2^2^3 ans = 3.138428376721003 1.1^2^2^2 ans = 2.143588810000001 p=12; sqrtsq([1.1 1.5 2], p) ans = 1.100000000000000 Inf Inf p=13; sqrtsq([1.1 1.5 2], p) ans = Inf Inf Inf p=5; sqsqrt([0 .1 .5 .9 1], p) ans = Columns 1 through 4 0 0.100000000000000 0.499999999999999 0.900000000000002 Column 5 1.000000000000000 p=8; sqsqrt([.1 .5 .9 1], p) ans = 0.099999999999999 0.499999999999999 0.899999999999999 1.000000000000000 p=9; sqsqrt([.1 .5 .9 1], p) ans = 0.100000000000002 0.499999999999999 0.899999999999999 1.000000000000000 p=10; sqsqrt([.1 .5 .9 1], p) ans = 0.100000000000002 0.499999999999999 0.899999999999999 1.000000000000000 p=13; sqsqrt([.1 .5 .9 1], p) ans = 0.100000000000002 0.500000000000114 0.899999999999792 1.000000000000000 p=20; sqsqrt([.1 .5 .9 1], p) ans = 0.099999999997554 0.500000000037885 0.900000000072656 1.000000000000000 p=30; sqsqrt([.1 .5 .9 1], p) ans = 0.099999996702750 0.499999997185433 0.899999898965448 1.000000000000000 p=40; sqsqrt([.1 .5 .9 1], p) ans = 0.099997278773432 0.499954938319014 0.899902593657302 1.000000000000000 p=40; sqsqrt([.1 .5 .9 1], p) ans = 0.099997278773432 0.499954938319014 0.899902593657302 1.000000000000000 p=50; sqsqrt([.1 .5 .9 1], p) ans = 0.093014488603712 0.472366550102742 0.882496901763774 1.000000000000000 p=60; sqsqrt([.1 .5 .9 1], p) ans = 0.000000000000000 0.000000000000000 0.000000000000000 1.000000000000000 n=10; t = single(0); for i=1:n, t = 1 + 1/single(i)^2, end t = 2 t = 1.2500000 t = 1.1111112 t = 1.0625000 t = 1.0400000 t = 1.0277778 t = 1.0204082 t = 1.0156250 t = 1.0123457 t = 1.0100000 n=100; t = single(0); for i=1:n, t = 1 + 1/single(i)^2, end t = 2 t = 1.2500000 t = 1.1111112 t = 1.0625000 t = 1.0400000 t = 1.0277778 t = 1.0204082 t = 1.0156250 t = 1.0123457 t = 1.0100000 t = 1.0082644 t = 1.0069444 t = 1.0059172 t = 1.0051020 t = 1.0044445 t = 1.0039062 t = 1.0034602 t = 1.0030864 t = 1.0027701 t = 1.0025001 t = 1.0022676 t = 1.0020661 t = 1.0018903 t = 1.0017362 t = 1.0016000 t = 1.0014793 t = 1.0013717 t = 1.0012755 t = 1.0011891 t = 1.0011111 t = 1.0010406 t = 1.0009766 t = 1.0009183 t = 1.0008651 t = 1.0008163 t = 1.0007716 t = 1.0007305 t = 1.0006925 t = 1.0006574 t = 1.0006250 t = 1.0005949 t = 1.0005668 t = 1.0005409 t = 1.0005165 t = 1.0004939 t = 1.0004725 t = 1.0004526 t = 1.0004340 t = 1.0004165 t = 1.0003999 t = 1.0003844 t = 1.0003698 t = 1.0003560 t = 1.0003430 t = 1.0003306 t = 1.0003189 t = 1.0003078 t = 1.0002973 t = 1.0002873 t = 1.0002778 t = 1.0002687 t = 1.0002601 t = 1.0002520 t = 1.0002441 t = 1.0002366 t = 1.0002296 t = 1.0002228 t = 1.0002162 t = 1.0002100 t = 1.0002041 t = 1.0001984 t = 1.0001929 t = 1.0001876 t = 1.0001826 t = 1.0001777 t = 1.0001731 t = 1.0001687 t = 1.0001644 t = 1.0001602 t = 1.0001563 t = 1.0001525 t = 1.0001488 t = 1.0001452 t = 1.0001417 t = 1.0001384 t = 1.0001352 t = 1.0001321 t = 1.0001291 t = 1.0001262 t = 1.0001235 t = 1.0001208 t = 1.0001181 t = 1.0001156 t = 1.0001131 t = 1.0001107 t = 1.0001085 t = 1.0001063 t = 1.0001041 t = 1.0001020 t = 1.0001000 n=100; t = single(0); for i=1:n, t = t + 1/single(i)^2, end t = 1 t = 1.2500000 t = 1.3611112 t = 1.4236112 t = 1.4636111 t = 1.4913889 t = 1.5117971 t = 1.5274221 t = 1.5397677 t = 1.5497677 t = 1.5580322 t = 1.5649766 t = 1.5708938 t = 1.5759958 t = 1.5804403 t = 1.5843465 t = 1.5878067 t = 1.5908931 t = 1.5936632 t = 1.5961633 t = 1.5984309 t = 1.6004970 t = 1.6023873 t = 1.6041235 t = 1.6057235 t = 1.6072028 t = 1.6085745 t = 1.6098500 t = 1.6110392 t = 1.6121503 t = 1.6131909 t = 1.6141675 t = 1.6150857 t = 1.6159508 t = 1.6167672 t = 1.6175388 t = 1.6182693 t = 1.6189618 t = 1.6196193 t = 1.6202443 t = 1.6208391 t = 1.6214060 t = 1.6219468 t = 1.6224633 t = 1.6229572 t = 1.6234298 t = 1.6238824 t = 1.6243165 t = 1.6247330 t = 1.6251329 t = 1.6255174 t = 1.6258872 t = 1.6262431 t = 1.6265861 t = 1.6269166 t = 1.6272355 t = 1.6275433 t = 1.6278406 t = 1.6281279 t = 1.6284057 t = 1.6286744 t = 1.6289345 t = 1.6291865 t = 1.6294307 t = 1.6296673 t = 1.6298969 t = 1.6301197 t = 1.6303359 t = 1.6305460 t = 1.6307501 t = 1.6309484 t = 1.6311413 t = 1.6313289 t = 1.6315116 t = 1.6316893 t = 1.6318624 t = 1.6320311 t = 1.6321955 t = 1.6323557 t = 1.6325120 t = 1.6326644 t = 1.6328132 t = 1.6329584 t = 1.6331002 t = 1.6332386 t = 1.6333737 t = 1.6335058 t = 1.6336349 t = 1.6337612 t = 1.6338847 t = 1.6340054 t = 1.6341236 t = 1.6342392 t = 1.6343523 t = 1.6344631 t = 1.6345716 t = 1.6346779 t = 1.6347820 t = 1.6348840 t = 1.6349840 n=100; t = single(0); for i=1:n, t = t + 1/single(i)^2, end; abs(t-pi^2/6)/t t = 1 t = 1.2500000 t = 1.3611112 t = 1.4236112 t = 1.4636111 t = 1.4913889 t = 1.5117971 t = 1.5274221 t = 1.5397677 t = 1.5497677 t = 1.5580322 t = 1.5649766 t = 1.5708938 t = 1.5759958 t = 1.5804403 t = 1.5843465 t = 1.5878067 t = 1.5908931 t = 1.5936632 t = 1.5961633 t = 1.5984309 t = 1.6004970 t = 1.6023873 t = 1.6041235 t = 1.6057235 t = 1.6072028 t = 1.6085745 t = 1.6098500 t = 1.6110392 t = 1.6121503 t = 1.6131909 t = 1.6141675 t = 1.6150857 t = 1.6159508 t = 1.6167672 t = 1.6175388 t = 1.6182693 t = 1.6189618 t = 1.6196193 t = 1.6202443 t = 1.6208391 t = 1.6214060 t = 1.6219468 t = 1.6224633 t = 1.6229572 t = 1.6234298 t = 1.6238824 t = 1.6243165 t = 1.6247330 t = 1.6251329 t = 1.6255174 t = 1.6258872 t = 1.6262431 t = 1.6265861 t = 1.6269166 t = 1.6272355 t = 1.6275433 t = 1.6278406 t = 1.6281279 t = 1.6284057 t = 1.6286744 t = 1.6289345 t = 1.6291865 t = 1.6294307 t = 1.6296673 t = 1.6298969 t = 1.6301197 t = 1.6303359 t = 1.6305460 t = 1.6307501 t = 1.6309484 t = 1.6311413 t = 1.6313289 t = 1.6315116 t = 1.6316893 t = 1.6318624 t = 1.6320311 t = 1.6321955 t = 1.6323557 t = 1.6325120 t = 1.6326644 t = 1.6328132 t = 1.6329584 t = 1.6331002 t = 1.6332386 t = 1.6333737 t = 1.6335058 t = 1.6336349 t = 1.6337612 t = 1.6338847 t = 1.6340054 t = 1.6341236 t = 1.6342392 t = 1.6343523 t = 1.6344631 t = 1.6345716 t = 1.6346779 t = 1.6347820 t = 1.6348840 t = 1.6349840 ans = 0.0060857 n=1000; t = single(0); for i=1:n, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 6.0782273e-04 n=10000; t = single(0); for i=1:n, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 1.2691732e-04 n=100000; t = single(0); for i=1:n, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 1.2691732e-04 n=100000; t = single(0); for i=1:n, t = t + 1/single(i)^2; end; t t = 1.6447253 n=10000; t = single(0); for i=1:n, t = t + 1/single(i)^2; end; t t = 1.6447253 n=100; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2, end; t t = 9.9999997e-05 t = 2.0203041e-04 t = 3.0615370e-04 t = 4.1243492e-04 t = 5.2094186e-04 t = 6.3174521e-04 t = 7.4491859e-04 t = 8.6053892e-04 t = 9.7868638e-04 t = 0.0010994 t = 0.0012229 t = 0.0013491 t = 0.0014783 t = 0.0016104 t = 0.0017456 t = 0.0018840 t = 0.0020257 t = 0.0021709 t = 0.0023196 t = 0.0024720 t = 0.0026283 t = 0.0027885 t = 0.0029529 t = 0.0031215 t = 0.0032947 t = 0.0034725 t = 0.0036551 t = 0.0038427 t = 0.0040356 t = 0.0042340 t = 0.0044381 t = 0.0046481 t = 0.0048644 t = 0.0050871 t = 0.0053167 t = 0.0055534 t = 0.0057975 t = 0.0060495 t = 0.0063096 t = 0.0065784 t = 0.0068562 t = 0.0071434 t = 0.0074407 t = 0.0077485 t = 0.0080674 t = 0.0083979 t = 0.0087409 t = 0.0090969 t = 0.0094667 t = 0.0098512 t = 0.0102512 t = 0.0106677 t = 0.0111017 t = 0.0115544 t = 0.0120270 t = 0.0125208 t = 0.0130373 t = 0.0135782 t = 0.0141451 t = 0.0147399 t = 0.0153649 t = 0.0160224 t = 0.0167149 t = 0.0174454 t = 0.0182170 t = 0.0190333 t = 0.0198984 t = 0.0208166 t = 0.0217932 t = 0.0228338 t = 0.0239449 t = 0.0251340 t = 0.0264095 t = 0.0277812 t = 0.0292605 t = 0.0308605 t = 0.0325966 t = 0.0344870 t = 0.0365531 t = 0.0388207 t = 0.0413207 t = 0.0440907 t = 0.0471772 t = 0.0506374 t = 0.0545436 t = 0.0589881 t = 0.0640901 t = 0.0700073 t = 0.0769517 t = 0.0852162 t = 0.0952162 t = 0.1075618 t = 0.1231868 t = 0.1435950 t = 0.1713728 t = 0.2113728 t = 0.2738728 t = 0.3849839 t = 0.6349839 t = 1.6349839 t = 1.6349839 n=100; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; t t = 1.6349839 n=1000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; t t = 1.6439345 n=10000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; t t = 1.6448340 n=100000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; t t = 1.6449240 n=100; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 0.0060858 n=1000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 6.0804037e-04 n=10000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 6.0811759e-05 n=100000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 6.0928278e-06 n=1000000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 6.5749941e-07 n=10000000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 7.7734505e-08 n=20000000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 7.7734505e-08 n=50000000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 5.2639400e-09 n=100000000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 5.2639400e-09 n=300000000; t = single(0); for i=n:-1:1, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 5.2639400e-09 n=10000; t = single(0); for i=1:n, t = t + 1/single(i)^2; end; abs(t-pi^2/6)/t ans = 1.2691732e-04 clc n = 5; M = rand(n); [L,U,p]=lu(M) L = Columns 1 through 4 1.000000000000000 0 0 0 0.891991704091174 1.000000000000000 0 0 0.139030187233434 -0.546904230755277 1.000000000000000 0 0.991696825559350 0.887000551296923 0.992383513999890 1.000000000000000 0.692331904741263 -0.399149960451055 0.479417567329872 0.147637192883412 Column 5 0 0 0 0 1.000000000000000 U = Columns 1 through 4 0.913375856139019 0.957506835434298 0.485375648722841 0.792207329559554 0 -0.756547748818577 -0.275337970351098 -0.564756027260130 0 0 0.739101580049873 0.496727331179596 0 0 0 -0.355873318170584 0 0 0 0 Column 5 0.933993247757551 -0.177373529520321 0.622269716039622 -1.350726249309949 -0.137606408355496 p = 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 format short n = 5; M = rand(n); [L,U,p]=lu(M) L = 1.0000 0 0 0 0 0.9807 1.0000 0 0 0 0.8650 0.8547 1.0000 0 0 0.5176 0.1340 -0.2813 1.0000 0 0.2259 0.0944 -0.4216 0.4234 1.0000 U = 0.7577 0.7060 0.8235 0.4387 0.4898 0 -0.6606 -0.1128 -0.0487 -0.0347 0 0 0.3343 0.4573 0.3154 0 0 0 0.6736 0.4862 0 0 0 0 0.5745 p = 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 norm(L*U - p*M) ans = 1.5701e-16 n = 50; M = rand(n); [L,U,p]=lu(M) L = Columns 1 through 8 1.0000 0 0 0 0 0 0 0 0.1444 1.0000 0 0 0 0 0 0 0.9682 0.5873 1.0000 0 0 0 0 0 0.9995 0.5876 0.9044 1.0000 0 0 0 0 0.3664 0.3497 -0.1297 -0.3573 1.0000 0 0 0 0.9557 -0.1104 -0.5683 0.8072 -0.8834 1.0000 0 0 0.6098 0.5519 0.4132 -0.0697 0.4473 -0.2778 1.0000 0 0.2978 0.0603 -0.0346 0.1975 -0.7240 0.2969 0.8024 1.0000 0.4891 -0.0055 -0.4292 -0.2227 -0.2353 -0.0229 0.0686 -0.2163 0.9732 0.1523 0.0245 -0.0938 0.4698 0.2607 0.3387 0.0235 0.5193 0.4858 0.1553 -0.6233 0.4386 0.1172 0.1405 0.6226 0.1354 0.0421 -0.2723 -0.8417 0.7027 -0.2429 0.0848 0.5177 0.6826 0.1375 -0.6702 -0.3107 0.5781 0.6708 -0.0282 0.2589 0.5927 0.0877 -0.2800 0.0351 -0.7262 0.3324 -0.2449 0.3997 0.3513 0.1540 -0.6567 -0.2241 0.2447 0.0194 -0.2575 -0.2476 0.8760 -0.1291 -0.0687 0.6104 0.1980 0.3746 0.7501 0.3528 0.2616 0.3454 -0.4039 0.1645 0.1201 0.3049 -0.5117 -0.1079 0.9283 -0.0957 0.1594 -0.0415 0.7080 -0.3127 0.6784 0.0766 0.3547 0.5853 -0.3051 -0.3036 0.6660 -0.0296 -0.6295 -0.7069 0.7284 0.7533 0.6435 0.6271 -0.5657 0.0476 -0.1202 0.2235 0.2876 0.0903 -0.2916 -0.5410 -0.5659 0.3654 -0.4394 0.5609 0.7082 0.6346 0.9370 0.4066 -0.2617 -0.3242 0.5273 -0.1027 0.2332 0.7168 0.7566 -0.4462 -0.6329 -0.1421 -0.7079 0.3654 0.1694 0.5051 -0.5255 -0.5150 0.9171 0.3639 -0.2256 0.1219 0.3647 0.8066 0.8398 -0.8152 -0.0259 -0.4162 -0.5755 0.1878 0.0562 0.6338 -0.2224 -0.2615 0.5664 -0.2483 0.6116 0.0029 0.2048 0.0319 -0.6746 -0.3795 -0.5506 0.3055 0.0138 0.5133 0.6419 0.0951 -0.4220 0.4021 -0.4537 0.3975 -0.2604 -0.0959 0.5916 -0.0111 0.1330 0.0190 -0.3586 0.0603 -0.0928 -0.0748 0.6098 0.0224 -0.6347 -0.1188 0.2619 0.6668 0.0270 0.3665 0.8118 0.3128 0.1496 0.9534 0.2881 0.0790 0.0229 -0.2884 0.4931 0.6997 0.4291 0.0917 0.5897 -0.2285 0.2893 0.2352 0.8484 -0.2280 -0.9079 0.3743 0.0306 0.4963 -0.2433 -0.6812 0.0124 0.1885 -0.7864 -0.3299 0.0103 0.3227 -0.6138 0.1959 0.2537 0.7391 0.9071 0.1335 -0.7863 -0.4988 0.0072 0.1657 0.5272 0.0943 0.0268 -0.0057 -0.7920 -0.1557 0.8521 0.5460 0.2649 0.9312 0.7116 -0.8552 0.4621 -0.4165 -0.2511 0.2847 0.5728 0.1181 0.1367 -0.2723 0.1185 -0.4162 0.4141 0.4896 0.5531 0.2145 -0.1290 -0.4234 -0.2148 0.3931 0.2320 0.8153 0.1556 0.0389 -0.5967 -0.1471 0.3685 0.3606 -0.2612 -0.1578 0.3964 0.4651 -0.2747 -0.0883 -0.2249 0.3145 -0.3266 0.3191 0.7890 0.6907 0.6424 0.6054 -0.2608 0.1568 0.0491 -0.1191 0.8657 0.7128 0.7870 0.7512 -0.5363 0.1429 -0.6210 0.0930 0.7853 0.3895 -0.0086 0.5256 -0.5657 0.6229 -0.7848 0.0246 0.5702 0.4054 -0.4673 0.3771 0.3624 0.5030 -0.3868 -0.2857 0.2683 0.3884 0.4692 -0.2301 -0.5188 -0.0447 0.6013 0.9837 0.0790 0.8686 -0.1403 0.0242 0.6329 -0.1812 0.3849 -0.2184 0.7828 0.2554 -0.3479 0.6514 0.6497 0.3145 -0.5104 -0.7299 0.1240 0.1389 -0.3954 -0.3378 -0.0660 0.0389 0.5086 0.7161 0.2658 0.0145 -0.3511 -0.1070 -0.8509 0.2091 0.1258 0.7118 Columns 9 through 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 0.3125 1.0000 0 0 0 0 0 0 -0.0418 0.6229 1.0000 0 0 0 0 0 -0.3557 -0.2557 -0.1119 1.0000 0 0 0 0 -0.3902 0.1486 -0.0990 0.1323 1.0000 0 0 0 0.5154 0.4135 0.6505 0.1261 0.0201 1.0000 0 0 0.2587 0.1118 0.4672 0.5698 -0.4336 -0.0599 1.0000 0 -0.5183 0.6700 -0.7173 -0.1723 -0.2979 -0.8835 -0.2473 1.0000 0.0384 -0.5000 0.2593 -0.0164 0.7480 0.6433 0.2514 0.1450 -0.2124 0.5061 -0.6378 0.0571 0.0505 -0.4586 0.3759 0.4330 0.6921 -0.2378 0.2526 -0.2789 0.2730 -0.2857 -0.3410 0.2347 -0.5949 -0.2310 -0.0031 0.3354 -0.5174 0.2001 0.1181 0.9111 0.7770 -0.1252 0.1635 -0.2272 0.7621 0.8875 0.0303 -0.3262 -0.1933 -0.2812 -0.3562 -0.4068 0.1634 0.0313 -0.4888 0.0538 -0.1215 -0.7152 0.3850 -0.0719 -0.0049 0.0911 0.6796 0.1506 -0.5023 0.2493 -0.0485 0.4641 -0.0266 -0.2590 -0.5956 -0.0865 0.5019 -0.6013 0.0129 0.1056 -0.1652 -0.0092 0.1870 -0.6183 -0.0907 0.0119 0.3596 -0.0167 0.5481 -0.3036 0.3869 0.3338 0.2462 -0.5684 -0.2712 0.1402 0.6251 0.1427 0.2527 -0.2318 0.1314 0.4156 -0.4360 -0.0270 -0.3649 -0.0826 -0.0747 0.1276 0.7047 -0.0545 0.0127 -0.2459 0.0402 0.1030 -0.0184 -0.3999 -0.0968 0.4369 0.0530 -0.0762 0.1665 0.0507 -0.4879 0.4097 -0.3309 0.6115 0.0929 0.0440 -0.2726 -0.5532 0.4711 0.8146 -0.3423 0.5032 -0.3885 0.1170 -0.4403 -0.4924 -0.5635 0.7206 0.1767 0.4287 -0.1836 0.2805 0.2479 -0.2190 -0.3574 0.0133 -0.4217 -0.4346 0.2798 0.9655 0.3971 0.3841 0.6909 -0.0358 0.1647 -0.9013 -0.4233 -0.2368 0.3050 0.2537 0.3089 -0.2091 0.0730 -0.1876 -0.6699 0.0248 -0.0214 0.0756 -0.4553 0.4340 0.2943 -0.1864 0.0114 0.2718 0.1977 0.2693 -0.4913 -0.4401 0.3219 0.2337 0.4894 0.2020 -0.4399 0.3016 0.2960 -0.3682 0.0758 0.1709 0.7459 0.4072 -0.1522 0.2005 0.7308 -0.6938 -0.0079 0.2266 -0.0897 -0.0166 0.0499 0.2521 -0.3029 0.4334 -0.1126 -0.2229 -0.1074 0.2641 0.6012 0.0722 -0.5274 0.1774 -0.1101 0.1195 -0.3857 -0.4533 -0.2618 -0.4409 -0.4299 0.5497 0.2209 0.6484 -0.0240 0.1509 -0.2791 0.1442 -0.0753 -0.0358 -0.3471 0.0140 -0.3381 0.4452 -0.1427 -0.0143 -0.2271 0.0403 -0.5415 0.4532 -0.4129 0.5612 -0.2923 -0.3189 -0.9593 0.5954 0.3482 0.2989 0.5944 -0.5525 0.4438 0.2682 0.3071 -0.0165 -0.4212 -0.2251 -0.2154 0.2494 0.3873 0.0427 -0.2191 -0.0987 -0.3038 0.3240 -0.6554 0.3384 0.0435 0.0898 -0.5081 0.7272 -0.4382 0.0296 -0.0475 0.3837 0.3459 -0.0439 0.0777 -0.0848 0.2570 -0.2620 0.1075 -0.2394 0.5530 0.5091 -0.0975 -0.0586 Columns 17 through 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 -0.4688 1.0000 0 0 0 0 0 0 0.6244 0.5268 1.0000 0 0 0 0 0 0.2237 0.3450 0.3838 1.0000 0 0 0 0 -0.1494 0.9573 -0.1782 -0.5232 1.0000 0 0 0 0.3676 -0.4624 0.0763 0.6223 -0.0839 1.0000 0 0 -0.2924 0.9242 0.2394 0.1700 0.5305 0.1398 1.0000 0 -0.3825 0.2420 0.3640 -0.6679 -0.6002 -0.0007 -0.4983 1.0000 -0.6477 0.5717 0.4028 -0.7384 0.1097 0.1042 0.8942 0.5740 0.4625 0.2493 0.6436 0.2952 -0.3306 -0.1080 -0.4253 0.1949 -0.2495 0.4655 -0.0977 -0.5139 -0.0267 -0.5689 -0.3207 0.0785 -0.7368 0.7847 0.1061 -0.2859 0.4639 -0.1420 0.0931 0.0142 0.1147 0.1776 0.3228 -0.0179 0.4917 -0.2436 0.2112 -0.2687 0.1173 -0.1804 -0.2942 0.1512 0.3484 0.1063 -0.3569 0.1731 0.1027 0.0380 0.6094 0.5829 -0.3184 0.9605 0.1009 0.3645 -0.3627 0.4318 0.4576 0.1247 -0.0836 0.1935 0.0273 0.5569 -0.1248 0.2411 0.4222 -0.3040 -0.0008 -0.0620 -0.7739 0.0970 -0.1257 0.8936 -0.1265 -0.9483 -0.0933 -0.3970 0.2551 0.2004 0.0224 0.3432 0.2028 0.2648 0.5350 0.2544 0.6259 -0.2313 -0.1580 -0.0853 -0.5063 0.0251 0.2174 0.2631 0.1597 -0.1759 -0.8464 0.9041 0.7057 -0.2422 0.1913 -0.5686 0.0053 0.3320 -0.6454 0.3692 -0.3657 -0.1819 0.3247 -0.8015 -0.4468 -0.3836 -0.7252 0.3870 -0.3043 -0.9651 -0.3332 -0.5488 0.4870 0.5299 0.2783 0.3650 0.2858 0.2231 0.3168 0.5217 -0.4019 0.3035 0.3930 -0.4151 -0.0025 -0.1526 -0.0216 0.2995 0.2294 -0.0843 -0.1011 0.6559 0.9289 0.4888 -0.0214 0.3610 0.9057 0.3259 -0.9779 0.6709 0.1482 -0.6618 0.1385 -0.2483 0.1377 0.2284 -0.7287 0.7365 0.2958 -0.3724 -0.0689 -0.4898 0.2250 0.2353 0.0849 0.1824 0.7398 -0.1141 -0.0730 -0.3027 -0.4023 0.4019 0.0387 0.2789 -0.0966 0.3531 0.5454 0.3542 0.3336 -0.0598 0.1688 0.3629 0.0478 -0.5016 -0.2102 -0.5511 -0.9765 0.1202 0.4240 0.0120 0.5439 0.3468 -0.2488 0.6167 -0.7276 0.4322 0.0518 -0.5620 -0.3556 -0.1937 -0.1281 0.4944 0.4047 0.1305 0.1774 -0.0852 -0.2213 0.1169 0.1577 0.2031 0.1091 -0.2068 Columns 25 through 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 -0.7055 1.0000 0 0 0 0 0 0 0.0351 -0.5117 1.0000 0 0 0 0 0 -0.4240 0.3059 0.3873 1.0000 0 0 0 0 -0.4203 -0.0854 -0.3724 -0.3166 1.0000 0 0 0 -0.7232 0.7140 -0.5168 0.7219 -0.2458 1.0000 0 0 -0.6520 0.5936 -0.5775 -0.0979 -0.5119 0.2566 1.0000 0 -0.4973 0.8560 -0.4665 0.5212 -0.3411 0.4556 0.2717 1.0000 -0.7066 0.0562 0.1306 -0.4626 0.9635 -0.1873 -0.4301 -0.4382 0.2506 0.4914 0.8707 -0.4406 -0.2421 -0.1406 0.1936 0.0636 -0.0217 -0.3142 0.0047 -0.2615 0.4300 -0.9349 -0.4455 0.0151 0.1059 0.1955 0.7124 0.3458 -0.3167 0.8254 0.1177 0.5889 0.2326 0.3286 0.3375 0.1254 0.3280 -0.3522 -0.4030 0.7471 -0.4990 -0.9400 0.2413 -0.1527 0.8961 -0.1940 -0.1047 -0.5128 0.5680 0.2519 0.3202 0.5545 -0.7144 0.7568 0.0950 0.6244 -0.7059 0.5712 -0.8050 0.5881 -0.3353 0.3373 -0.1643 -0.7429 0.5940 -0.3191 0.2109 -0.4927 -0.1956 -0.2637 -0.0421 0.7523 0.0361 0.8938 -0.9859 0.8513 -0.5728 -0.2806 -0.0899 0.4238 0.0363 -0.2952 0.7445 -0.4049 0.3201 -0.3453 0.2934 0.5299 0.2525 -0.0603 0.7843 -0.1975 0.0637 -0.2284 0.2118 0.3458 -0.5924 0.6255 -0.4042 -0.0436 0.8282 0.7198 -0.4193 0.8074 -0.1728 -0.1195 -0.4191 0.2406 -0.1225 -0.1578 0.2760 0.3237 -0.4073 0.1936 0.9574 0.0181 0.5750 -0.5592 -0.3991 0.2939 -0.2295 0.2555 -0.3006 -0.1108 -0.3894 -0.3706 0.1911 0.2744 0.0621 0.1534 -0.1845 -0.4764 0.3422 0.1110 0.0480 0.5474 0.0653 -0.4723 0.3780 -0.3396 0.2103 -0.8208 0.2593 -0.5484 Columns 33 through 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 0.5416 1.0000 0 0 0 0 0 0 0.2366 -0.0503 1.0000 0 0 0 0 0 0.1362 0.6798 -0.5000 1.0000 0 0 0 0 0.1202 0.0636 -0.2596 0.5205 1.0000 0 0 0 -0.0168 -0.7363 0.7248 -0.3215 0.7755 1.0000 0 0 -0.5704 0.2915 -0.9666 0.2886 0.0249 -0.6897 1.0000 0 0.3074 -0.6112 0.1287 -0.1200 0.7391 -0.0212 0.8822 1.0000 0.4419 0.4887 -0.0691 0.4987 -0.7397 -0.2585 -0.3932 -0.8610 -0.1186 -0.4935 0.3363 -0.2082 0.5921 0.2983 -0.4729 0.3010 0.2573 0.2728 0.7629 -0.6519 -0.8934 0.0687 0.4956 -0.1654 0.3483 0.4502 0.0574 -0.0761 0.8802 0.2550 -0.4785 0.0605 0.3678 0.1786 -0.7334 0.2474 -0.2998 -0.4903 0.1429 0.1212 -0.3964 -0.5243 0.1303 0.2059 0.4581 0.0201 0.8025 0.3253 0.0816 0.4844 0.1526 -0.3428 -0.1985 0.0442 -0.4524 -0.4339 -0.0975 0.3640 -0.0961 0.1110 -0.9701 -0.9226 0.6348 0.1459 0.0808 0.5553 -0.7818 0.8777 -0.6564 -0.5090 -0.2636 -0.5432 0.0622 0.0874 0.5555 0.3172 0.6120 0.6981 -0.9545 -0.4291 Columns 41 through 48 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 0.4652 1.0000 0 0 0 0 0 0 -0.6522 -0.2414 1.0000 0 0 0 0 0 -0.2243 0.5920 -0.1625 1.0000 0 0 0 0 -0.0813 0.2655 0.4654 0.7417 1.0000 0 0 0 -0.1387 -0.4738 0.4916 -0.6932 0.3054 1.0000 0 0 -0.0276 0.7406 0.5941 0.8100 0.3117 0.2645 1.0000 0 0.3087 -0.8854 -0.3627 -0.7882 0.3309 0.3213 -0.5924 1.0000 0.3447 -0.9753 -0.6179 -0.7236 0.1134 0.0944 0.0806 0.5883 0.5291 -0.3174 -0.9252 -0.6344 -0.8040 -0.2433 0.5941 0.6313 Columns 49 through 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 -0.1226 1.0000 U = Columns 1 through 8 0.9597 0.2630 0.3377 0.8759 0.6791 0.8181 0.1781 0.6385 0 0.9582 0.9074 0.0442 0.5816 0.7071 0.9559 0.2329 0 0 -0.8168 0.0308 -0.2841 -1.1470 -0.2518 -0.6014 0 0 0 -0.7346 -0.5018 0.2578 -0.1430 0.7374 0 0 0 0 -0.6378 -0.3117 -0.2315 0.3881 0 0 0 0 0 -1.6720 0.5275 -0.9380 0 0 0 0 0 0 0.7071 -0.5835 0 0 0 0 0 0 0 1.3331 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 9 through 16 0.3225 0.9398 0.3309 0.8790 0.6952 0.6628 0.2982 0.3288 0.6918 -0.0299 0.7073 0.7739 0.5399 0.6682 0.7827 0.3217 -0.6274 -0.2645 -0.2971 -1.2221 -0.8237 -0.6983 -0.1450 0.2646 0.4460 0.3111 -0.0808 -0.0002 -0.0587 -0.0090 -0.0931 -0.6708 0.3655 0.4392 0.0784 0.0177 0.1665 0.3418 0.2575 0.0461 -0.4165 -0.0538 -0.0725 -1.4163 0.1060 -0.0854 0.8018 0.7480 -0.0961 -0.1576 -0.2600 -0.8591 0.1051 0.2368 0.0526 0.4021 0.9271 0.5966 0.5584 0.8928 0.6072 0.0070 0.1212 -0.2496 0.7926 0.1803 0.3470 -0.5339 0.1103 -0.3619 -0.0345 0.5097 0 -1.0393 0.1972 0.2169 -0.6387 -0.3943 -0.0202 0.0197 0 0 -0.9454 -0.2616 -0.0691 -0.3358 -0.7872 -0.1455 0 0 0 -1.3445 -0.6039 -0.8540 -0.2987 0.2963 0 0 0 0 -1.1870 -0.8055 -0.2074 0.1129 0 0 0 0 0 1.2741 0.2550 0.3367 0 0 0 0 0 0 1.0411 0.3641 0 0 0 0 0 0 0 1.0863 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 17 through 24 0.7690 0.4024 0.9535 0.3872 0.5341 0.0427 0.6465 0.0423 0.5854 0.2360 0.2774 0.9015 0.2773 0.8235 0.2673 0.9687 -0.3654 -0.1056 -0.9226 -0.7237 -0.3433 -0.3317 0.0549 -0.2782 -0.4663 -0.0946 0.2648 0.3088 0.2301 0.0099 -0.5224 -0.3406 -0.6019 -0.1526 0.2805 0.1867 0.1566 -0.0311 -0.2284 0.4180 -0.7157 0.1768 -0.6996 -0.0204 -0.1706 0.3363 0.2535 1.2886 -0.3302 0.1809 0.0250 -0.4772 0.4607 0.4689 -0.0300 -0.1090 0.1732 0.5298 0.7211 1.0815 0.1448 0.3320 0.3403 0.7889 -0.4179 -0.0931 -0.1536 0.4195 -0.1975 0.2735 0.2084 0.1660 0.7493 0.2287 -0.3438 0.2597 -0.2041 0.0027 -0.6042 -0.0579 -0.6277 -0.1375 -0.4536 -0.5591 0.4837 0.1179 0.1787 -0.4653 0.2462 0.1610 -0.4691 0.4561 0.0958 0.7751 0.3012 0.0811 -0.4030 -0.4171 -0.2012 -0.1587 0.3660 -0.6166 -0.2382 -0.8741 -0.0936 -0.3794 0.8276 -0.9132 -0.1500 -0.5096 -0.6348 0.1881 0.0338 -0.1142 0.5923 -0.0390 0.3844 -0.1015 0.2022 0.1843 -0.9932 -0.7927 -0.5082 -1.4331 0.4552 -0.7417 0.2470 -0.3254 1.3524 1.4988 -0.4270 0.6378 -0.3902 0.6850 -0.0014 -0.0738 0 1.2366 -0.7984 0.7900 -1.0333 1.0655 0.1637 0.9460 0 0 1.4654 -0.9797 1.4440 -0.4856 0.2471 0.4423 0 0 0 1.4864 -0.9063 0.0218 -0.1339 -0.4001 0 0 0 0 1.8826 0.1195 0.2490 -1.2873 0 0 0 0 0 1.1277 0.5876 1.6089 0 0 0 0 0 0 -1.0955 -0.3061 0 0 0 0 0 0 0 -2.9026 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 25 through 32 0.4706 0.4170 0.5466 0.4279 0.0977 0.4249 0.8531 0.2794 0.7123 0.5386 -0.0185 0.3646 0.4910 0.1278 0.4254 0.6463 0.1069 0.1624 -0.4230 0.1058 0.2786 0.4530 -0.1193 -0.5924 -0.6232 0.0335 0.6790 -0.1756 0.2787 -0.6887 -0.6727 0.3271 0.3134 -0.0328 0.9908 -0.2240 0.8701 -0.3193 -0.5284 -0.0953 0.4954 0.5237 -0.0075 -0.3143 1.1956 1.0940 -0.1346 -0.6073 -0.5012 0.5318 -0.1505 0.1147 -0.3753 0.3771 0.3508 0.5208 0.8722 -0.3736 1.0218 -0.0433 1.0260 -0.4105 -0.2320 -0.3619 0.1957 0.4379 0.4250 -0.2221 1.0199 0.5601 -0.7254 0.1045 0.0567 -0.0336 -0.1382 -0.1501 -0.7867 -0.1646 -0.4352 0.4672 -1.2574 0.4243 -0.3550 0.1588 0.1298 -0.1445 -0.1344 0.3476 -0.2211 1.2074 0.1761 0.4730 0.0336 0.5204 -0.1831 0.5425 -0.3371 0.5318 -0.8267 0.7371 -0.0865 -0.4037 0.2386 0.6243 0.6987 -0.8006 0.0664 0.3358 0.2458 -0.2644 0.2937 -0.1010 0.2803 -0.4482 -0.1329 0.1262 0.1388 -0.1174 0.2931 -0.2237 -0.3808 -0.2095 -1.1733 0.9664 1.0143 -0.2102 0.1494 0.4341 0.4522 0.6417 1.1454 -0.0834 -0.4812 0.8447 0.0589 0.1692 0.1028 0.8553 0.3976 -0.5294 0.8017 0.3750 -0.4942 -0.6065 0.2013 -0.7340 -0.2147 1.0130 -0.4347 -0.9111 0.7437 0.4437 -0.5348 0.4247 0.9923 -1.1695 -0.4900 0.2339 -1.0103 0.5402 -1.6931 0.0164 0.3441 0.0964 -2.4090 -0.5279 -0.1573 1.9111 0.2712 0.1069 0.3109 0.3122 1.3378 -0.2433 -0.2601 -0.5757 0.6392 0.6809 1.0364 -0.0069 -0.2237 0.8057 -0.7217 0.6423 -1.2236 0.7246 0.9954 -0.4283 -1.9726 0.9173 -0.3835 1.6835 -1.6104 -0.6572 -0.7665 -0.4605 0.2894 -1.1391 0.3971 0.7986 0 -1.0142 0.1418 -0.8545 0.3300 0.2466 -0.2288 -0.1086 0 0 1.6116 -0.2638 -0.2765 0.3260 -0.8374 0.6419 0 0 0 1.0823 0.9344 -0.0899 0.7525 0.5238 0 0 0 0 1.8119 -0.0632 0.5535 0.5314 0 0 0 0 0 -0.8833 -0.1478 0.3946 0 0 0 0 0 0 1.4482 0.5201 0 0 0 0 0 0 0 -0.9237 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 33 through 40 0.2789 0.8277 0.4324 0.1792 0.2262 0.6249 0.6806 0.2871 0.6594 0.0502 0.9000 0.4034 0.8516 0.5278 0.6586 0.1722 -0.5672 -0.0259 -0.2421 0.5437 0.2804 -0.8802 -0.5048 0.0589 0.7054 -0.1620 0.2522 -0.0939 -0.4023 0.0178 -0.0821 -0.0860 0.3751 0.3296 0.5495 -0.0767 -0.3772 -0.3775 0.1740 0.7440 -0.4363 0.5966 0.4106 0.8329 0.3976 -0.9852 -0.0920 1.2973 -0.3025 -0.0722 -0.7353 0.1101 0.2895 0.3927 -0.2226 -0.2215 0.8143 -0.0230 1.1557 -0.4301 -0.4447 -0.1415 1.0459 0.5834 0.6953 0.0637 0.8466 0.0771 0.6386 -0.0175 0.4475 0.8886 -0.1967 -0.9372 -0.4577 -0.0537 -0.3247 0.3851 -0.0823 -0.2282 0.1424 0.1304 -0.8580 0.1970 -0.0212 0.4592 -0.9985 -0.5767 0.6716 0.4637 -0.4274 0.9696 0.5141 0.5708 -0.9420 -0.1965 0.4774 -0.1626 -0.9725 0.0136 0.9506 0.0954 -0.1904 -1.0724 0.0588 0.5530 -0.0378 -0.3388 0.1467 -0.1565 0.0747 0.5409 -0.6814 -0.2441 -0.1071 0.0566 0.8414 -0.9342 0.6563 -0.0075 0.7118 1.2743 0.0897 0.7671 1.9182 0.3638 -0.1293 -0.2937 -1.0420 -0.5437 0.7093 0.1424 -1.3855 0.1585 -0.1308 0.4752 -0.3180 -0.5370 0.6558 0.1908 -0.7652 0.3992 -0.9924 1.3235 0.3539 -0.1806 -1.1165 0.3516 0.5692 -0.3227 0.5005 -0.5260 -0.6547 -1.3344 -0.5353 -1.0687 -1.5677 0.0560 0.8736 0.1659 -0.2286 0.1262 -1.0068 0.1623 -0.8831 0.0603 0.6084 -1.4909 0.5990 0.9836 0.4214 0.6355 1.2689 0.2895 -1.0882 1.5932 1.1707 0.0086 0.5273 -0.0052 -0.7777 0.5729 -0.0257 0.3338 -0.3609 -1.3966 -0.4696 -0.3857 -0.8671 -0.0664 1.7220 -1.2103 -1.6493 0.1039 -1.0969 -0.4109 -0.0177 0.9413 -0.9609 0.2714 0.1877 2.1710 0.2278 0.1878 -1.1807 0.4605 -0.6928 1.4312 0.4148 1.1397 0.2469 0.7524 -1.6438 0.7957 -1.2455 1.0426 -1.1610 -1.2729 -0.4553 -1.0757 0.7497 -0.0465 -0.2018 -0.5162 -0.6488 0.5690 -0.1049 -0.0511 0.8137 0.8339 -1.4745 1.1273 0.1212 -0.4999 -0.9702 0.6120 0.6626 0.4546 -1.9345 0.9210 -2.1026 0.3051 -0.4548 -0.7553 -0.7237 0.5330 -1.4593 -0.2499 -0.8069 0.3270 -0.0766 -0.2709 0.0113 -0.7430 -0.0366 -0.2913 -2.1356 -1.8368 -0.2764 -1.7301 -1.2291 -0.5240 0.4577 -0.4096 0 -2.2589 -0.9242 -1.2955 2.6969 -0.7673 2.8747 -1.2030 0 0 -1.3974 0.9927 0.6533 1.3694 -2.9522 1.4678 0 0 0 1.9070 -0.6396 -0.0097 -0.6468 0.3190 0 0 0 0 1.3271 0.7935 -0.8352 1.0487 0 0 0 0 0 -2.5299 4.9589 -1.4587 0 0 0 0 0 0 1.8864 0.7271 0 0 0 0 0 0 0 -2.5328 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 41 through 48 0.3545 0.8876 0.4484 0.7025 0.4926 0.3264 0.3964 0.8960 0.2251 0.4899 -0.0126 0.8523 0.0498 0.7074 0.0980 0.2423 -0.3853 -0.1851 -0.3677 -1.0289 0.0769 -0.3246 -0.3104 -0.2760 0.4348 -0.8992 0.5926 0.6743 -0.2262 0.2084 0.4207 -0.4563 0.5166 0.0482 0.7558 0.3816 0.0712 -0.0845 0.3355 -0.4551 -0.2313 0.1799 0.3795 -1.0832 0.7616 -0.0696 -0.3732 -0.7730 0.1259 -0.3740 0.2079 -0.4538 0.6944 -0.3048 -0.0805 -0.0646 0.4271 0.3873 0.6318 1.2318 -0.7863 0.2151 0.7205 0.0616 0.8194 0.2623 0.7008 -0.1360 -0.3491 0.2955 0.7383 -0.2067 0.1535 -0.2689 -0.2019 0.2927 -0.7805 0.1816 -0.5510 0.2556 0.3340 -0.6439 0.1561 -0.5868 1.2359 0.0369 0.1878 -0.7152 0.8930 -1.0405 -0.1619 -0.7527 0.1954 0.9635 0.1731 -0.3587 0.3659 -0.1862 -0.6453 -0.4285 -0.5411 0.2211 0.8461 -0.2261 -0.2202 0.6478 0.0679 0.3546 0.4899 -0.0091 -0.2321 0.4683 -0.4151 0.5542 0.2029 -0.0551 -0.7017 -0.3084 0.6607 0.5414 0.6564 0.9638 0.0069 -0.6216 0.8677 0.3242 0.9445 -0.3310 0.0108 -0.3933 0.0250 -0.0611 -0.0740 -0.1067 -0.4406 0.9842 0.1878 -0.5485 0.2213 -0.4914 1.4789 0.3704 -1.0084 0.0885 -0.7127 -0.3606 -0.4498 1.1425 -0.8275 -0.1640 0.3514 0.1972 0.3148 0.2370 0.5303 -0.0238 -1.4258 -0.9867 0.0284 -0.7742 0.1260 -0.2529 0.2219 0.0934 -1.6145 -1.2671 1.0103 -0.2751 0.7720 -0.2316 0.7870 -0.0802 1.4851 1.5758 0.3723 -0.4254 1.2914 -0.1419 0.6168 0.2958 0.0985 0.2143 -0.0112 0.3041 0.4248 0.7969 1.2826 -0.2163 -1.6503 -1.6110 1.2985 0.9690 0.2319 -0.5753 0.0286 -0.1043 0.6166 0.3620 0.0465 -1.4597 0.3844 -0.1928 0.1650 0.1251 1.4291 0.6458 -0.7125 -1.0232 1.7738 -1.0756 1.2529 0.7732 0.8421 0.4694 -0.1401 -1.1770 -0.1609 0.3139 -0.6525 -1.0861 -0.7989 0.2858 0.6552 0.1845 1.8836 -0.2907 0.3557 -0.4492 1.9489 1.6036 0.4458 -0.8688 0.8579 -2.2429 0.9236 1.1331 1.2229 0.4122 -0.3400 -0.6835 0.3275 -0.0908 -1.3875 -0.4254 0.1049 -0.3602 -0.5438 -0.4046 -0.3191 -0.6039 -0.1647 -0.7842 0.7227 0.0346 0.5205 -0.2098 -0.9948 0.3005 -0.5240 -0.0762 -1.4859 -1.2772 -0.1771 -0.4581 -0.8799 0.9984 0.3209 -0.2615 -2.5389 -0.8595 1.3843 1.6001 0.7735 -2.1904 0.5863 0.1857 2.2343 0.7287 -0.5373 -0.7222 -0.9150 0.9148 -0.8372 0.0933 0.6710 0.7577 -1.2031 0.1548 0.4503 -0.8720 1.3870 0.5776 0.6647 0.0089 0.6052 1.0172 -2.1276 2.4216 -1.8889 -0.9590 -3.2262 -0.8051 0.8353 0.7640 -0.4127 1.5948 -2.0177 -0.0571 -1.5271 -0.1775 0.6096 -1.2130 1.2091 -1.0583 0.8648 -0.7488 1.5690 0.8402 -0.2950 0.6851 2.0189 -1.3059 1.7529 -0.4817 1.9422 0.1615 0.0809 0.8498 0 1.3450 -1.4467 1.3081 -2.4247 0.0989 0.8760 -2.1178 0 0 2.0758 0.2747 1.4927 0.2232 -0.3278 2.5254 0 0 0 -1.4185 1.4775 0.4986 -0.5834 1.0131 0 0 0 0 -2.7693 -1.9862 0.7465 -0.1438 0 0 0 0 0 0.9490 -1.0793 -1.2522 0 0 0 0 0 0 -0.6535 -0.9541 0 0 0 0 0 0 0 0.7252 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 49 through 50 0.4668 0.5677 0.4548 0.3421 0.1394 -0.4101 -0.6381 -0.1368 0.2315 0.1982 0.9887 -0.3688 -0.0353 0.2767 0.0410 0.1339 0.2822 -0.2046 -0.2935 -0.1707 0.0030 -0.1691 0.2001 -0.2769 -0.8090 -0.1569 0.3013 0.6158 -0.2373 -0.1439 0.0612 0.6735 0.3893 0.3132 0.7244 -0.6502 -1.0703 0.6707 -0.1172 -1.1584 -0.5690 0.8436 0.6898 0.2557 0.0087 1.0737 -0.6695 0.2312 -0.4233 -1.4346 1.2949 -0.2260 1.1322 0.6302 -1.2076 -0.7985 0.9267 -0.7137 0.0400 -0.2368 0.3973 -0.3599 -0.0648 -0.0503 -0.9415 -0.3826 -1.8222 -0.8790 0.2874 -0.4697 1.2242 -0.6000 -0.1114 0.6183 -1.7926 -0.1554 -1.2825 0.5157 1.1714 -1.6690 0.4097 -0.3052 0.9689 0.2967 1.9265 -0.1631 0.0110 0.3859 -2.3389 -0.5272 0.8523 0.1832 -1.1660 -0.6886 0.7603 1.1228 0.5063 -0.0987 0 -0.4907 p = Columns 1 through 14 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 43 through 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 norm(L*U - p*M) ans = 2.9478e-15 n = 5; M = rand(n); b=rand(n,1); [L,U,p]=lu(M) L = 1.0000 0 0 0 0 0.9698 1.0000 0 0 0 0.8012 -0.4441 1.0000 0 0 0.2625 0.2065 -0.8914 1.0000 0 0.9825 0.5366 0.4014 -0.2921 1.0000 U = 0.8884 0.9380 0.8964 0.5274 0.2442 0 -0.5158 -0.8553 0.0959 -0.2266 0 0 -0.4751 0.2084 0.3126 0 0 0 0.7525 0.6903 0 0 0 0 0.9159 p = 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 n = 5; M = rand(n); b=rand(n,1); [L,U,p]=lu(M); y=L\b; x=U\y x = -2.3469 2.5620 6.9820 -5.9886 -0.5768 n = 5; M = rand(n); b=rand(n,1); [L,U,p]=lu(M); y=L\b; x=U\y x = 1.2599 0.4021 1.1404 -1.4113 -1.0654 norm( p*A*x-b ) {??? Undefined function or variable 'A'. } norm( p*M*x-b ) ans = 3.8459e-16 n = 5; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000265 seconds. n = 5; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000233 seconds. n = 5; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000237 seconds. n = 5; M = rand(n); b=rand(n,1); tic; x = inv(M)*b; toc Elapsed time is 0.000711 seconds. n = 5; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000230 seconds. n = 5; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000240 seconds. n = 5; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000230 seconds. n = 5; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000234 seconds. n = 50; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000384 seconds. n = 50; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000267 seconds. n = 50; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000341 seconds. n = 50; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000361 seconds. n = 50; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000367 seconds. n = 50; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000338 seconds. n = 50; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000349 seconds. n = 50; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.000429 seconds. n = 50; M = rand(n); b=rand(n,1); tic; x = inv(M)*b; toc Elapsed time is 0.000494 seconds. n = 50; M = rand(n); b=rand(n,1); tic; x = inv(M)*b; toc Elapsed time is 0.000486 seconds. n = 50; M = rand(n); b=rand(n,1); tic; x = inv(M)*b; toc Elapsed time is 0.000362 seconds. n = 100; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.013369 seconds. n = 100; M = rand(n); b=rand(n,1); tic; x = inv(M)*b; toc Elapsed time is 0.042050 seconds. n = 500; M = rand(n); b=rand(n,1); tic; x = inv(M)*b; toc Elapsed time is 0.072048 seconds. n = 500; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.039289 seconds. n = 1000; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.134163 seconds. n = 1000; M = rand(n); b=rand(n,1); tic; x = inv(M)*b; toc Elapsed time is 0.301684 seconds. n = 2000; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 0.739523 seconds. n = 2000; M = rand(n); b=rand(n,1); tic; x = inv(M)*b; toc Elapsed time is 2.286041 seconds. n = 3000; M = rand(n); b=rand(n,1); tic; [L,U,p]=lu(M); y=L\b; x=U\y; toc Elapsed time is 2.274591 seconds. n = 3000; M = rand(n); b=rand(n,1); tic; x = inv(M)*b; toc Elapsed time is 6.296742 seconds. diary