octave:2> A=[1,1;1,1;2,1] A = 1 1 1 1 2 1 octave:3> b=[1;2;0] b = 1 2 0 octave:4> rank(A) ans = 2 octave:5> rank([A,b]) ans = 3 octave:6> A\b ans = -1.5000 3.0000 octave:7> (A'*A)\(A'*b) ans = -1.5000 3.0000 octave:8> x=linspace(0,10,11); octave:9> y=x+1; octave:10> y=y+(rand(size(y))-0.5)/5; octave:11> plot(x,y,'*') octave:12> V=[x';ones(size(x))'] V = 0 1 2 3 4 5 6 7 8 9 10 1 1 1 1 1 1 1 1 1 1 1 octave:13> V=[x',ones(size(x))'] V = 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 octave:14> V=[x',ones(size(x))']; octave:15> y y = Columns 1 through 7: 1.0645 1.9617 2.9305 3.9564 4.9944 6.0037 6.9336 Columns 8 through 11: 8.0518 8.9884 10.0762 11.0534 octave:16> y' ans = 1.0645 1.9617 2.9305 3.9564 4.9944 6.0037 6.9336 8.0518 8.9884 10.0762 11.0534 octave:17> a=V\(y') a = 1.00642 0.96925 octave:18> xx=linspace(0,10,100); octave:19> yy=polyval(a,xx); octave:20> plot(x,y,'*',xx,yy) octave:21> vander(x) ans = Columns 1 through 5: 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0240e+03 5.1200e+02 2.5600e+02 1.2800e+02 6.4000e+01 5.9049e+04 1.9683e+04 6.5610e+03 2.1870e+03 7.2900e+02 1.0486e+06 2.6214e+05 6.5536e+04 1.6384e+04 4.0960e+03 9.7656e+06 1.9531e+06 3.9062e+05 7.8125e+04 1.5625e+04 6.0466e+07 1.0078e+07 1.6796e+06 2.7994e+05 4.6656e+04 2.8248e+08 4.0354e+07 5.7648e+06 8.2354e+05 1.1765e+05 1.0737e+09 1.3422e+08 1.6777e+07 2.0972e+06 2.6214e+05 3.4868e+09 3.8742e+08 4.3047e+07 4.7830e+06 5.3144e+05 1.0000e+10 1.0000e+09 1.0000e+08 1.0000e+07 1.0000e+06 Columns 6 through 10: 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 3.2000e+01 1.6000e+01 8.0000e+00 4.0000e+00 2.0000e+00 2.4300e+02 8.1000e+01 2.7000e+01 9.0000e+00 3.0000e+00 1.0240e+03 2.5600e+02 6.4000e+01 1.6000e+01 4.0000e+00 3.1250e+03 6.2500e+02 1.2500e+02 2.5000e+01 5.0000e+00 7.7760e+03 1.2960e+03 2.1600e+02 3.6000e+01 6.0000e+00 1.6807e+04 2.4010e+03 3.4300e+02 4.9000e+01 7.0000e+00 3.2768e+04 4.0960e+03 5.1200e+02 6.4000e+01 8.0000e+00 5.9049e+04 6.5610e+03 7.2900e+02 8.1000e+01 9.0000e+00 1.0000e+05 1.0000e+04 1.0000e+03 1.0000e+02 1.0000e+01 Column 11: 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00 octave:22> polyfit(x,y,1) ans = 1.00642 0.96925 octave:23> a(1)*xx+a(2) ans = Columns 1 through 6: 0.96925 1.07091 1.17257 1.27422 1.37588 1.47754 Columns 7 through 12: 1.57920 1.68086 1.78252 1.88418 1.98583 2.08749 Columns 13 through 18: 2.18915 2.29081 2.39247 2.49413 2.59578 2.69744 Columns 19 through 24: 2.79910 2.90076 3.00242 3.10408 3.20574 3.30739 Columns 25 through 30: 3.40905 3.51071 3.61237 3.71403 3.81569 3.91735 Columns 31 through 36: 4.01900 4.12066 4.22232 4.32398 4.42564 4.52730 Columns 37 through 42: 4.62896 4.73061 4.83227 4.93393 5.03559 5.13725 Columns 43 through 48: 5.23891 5.34057 5.44222 5.54388 5.64554 5.74720 Columns 49 through 54: 5.84886 5.95052 6.05217 6.15383 6.25549 6.35715 Columns 55 through 60: 6.45881 6.56047 6.66213 6.76378 6.86544 6.96710 Columns 61 through 66: 7.06876 7.17042 7.27208 7.37374 7.47539 7.57705 Columns 67 through 72: 7.67871 7.78037 7.88203 7.98369 8.08535 8.18700 Columns 73 through 78: 8.28866 8.39032 8.49198 8.59364 8.69530 8.79695 Columns 79 through 84: 8.89861 9.00027 9.10193 9.20359 9.30525 9.40691 Columns 85 through 90: 9.50856 9.61022 9.71188 9.81354 9.91520 10.01686 Columns 91 through 96: 10.11852 10.22017 10.32183 10.42349 10.52515 10.62681 Columns 97 through 100: 10.72847 10.83013 10.93178 11.03344 octave:24> quit