Algorithmic Gaussian Elimination
\302\251Mike May, S.J., 2005, Saint Louis University
restart:
with(LinearAlgebra):
One of the strengths of Gaussian Elimination is that it can be done mechanically to a randomly chosen matrix. It is worthwhile to see that it works in this mode.
We will assume that the reduction can be done without any row swapping. We print out the result after full use of each pivot.
rsize := 7: csize := 8:
M1 := RandomMatrix(rsize, csize, generator = rand(10)):
M[0] := M1:
for i from 1 to rsize do:
M[i] := M[i-1]:
for j from i+1 to rsize do:
M[i] := RowOperation(M[i],[j,i],-M[i][j,i]/M[i][i,i]);
end do;
end do;
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
NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSVtc3ViR0YlNiYtSSNtaUdGJTY5USJNRigvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GKC8lJXNpemVHUSMxMkYoLyUlYm9sZEdRJmZhbHNlRigvJSdpdGFsaWNHUSV0cnVlRigvJSp1bmRlcmxpbmVHRjsvJSpzdWJzY3JpcHRHRjsvJSxzdXBlcnNjcmlwdEdGOy8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GKC8lK2JhY2tncm91bmRHUShbMCwwLDBdRigvJSdvcGFxdWVHRjsvJStleGVjdXRhYmxlR0Y7LyUpcmVhZG9ubHlHRj4vJSljb21wb3NlZEdGOy8lKmNvbnZlcnRlZEdGOy8lK2ltc2VsZWN0ZWRHRjsvJSxwbGFjZWhvbGRlckdGOy8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYoLyUqbWF0aGNvbG9yR0ZHLyUvbWF0aGJhY2tncm91bmRHRkovJStmb250ZmFtaWx5R0Y1LyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGKC8lKW1hdGhzaXplR0Y4LUYkNiMtSSNtbkdGJTY5USIzRihGM0Y2RjkvRj1GO0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuL0Zdb1Enbm9ybWFsRihGX28vJS9zdWJzY3JpcHRzaGlmdEdRIjBGKC8lLHBsYWNlaG9sZGVyR0Y7LUkjbW9HRiU2M1EjOj1GKC8lJWZvcm1HUSZpbmZpeEYoLyUmZmVuY2VHRjsvJSpzZXBhcmF0b3JHRjsvJSdsc3BhY2VHUS90aGlja21hdGhzcGFjZUYoLyUncnNwYWNlR0ZccS8lKXN0cmV0Y2h5R0Y7LyUqc3ltbWV0cmljR0Y7LyUobWF4c2l6ZUdRKWluZmluaXR5RigvJShtaW5zaXplR1EiMUYoLyUobGFyZ2VvcEdGOy8lLm1vdmFibGVsaW1pdHNHRjsvJSdhY2NlbnRHRjsvJTBmb250X3N0eWxlX25hbWVHRmVuLyUlc2l6ZUdGOC8lK2ZvcmVncm91bmRHRkcvJStiYWNrZ3JvdW5kR0ZKLUYkNiUtRmBwNjNRIltGKC9GZHBRJ3ByZWZpeEYoL0ZncEY+RmhwL0ZbcVEudGhpbm1hdGhzcGFjZUYoL0ZecUZgcy9GYHFGPkZhcUZjcUZmcUZpcUZbckZdckZfckZhckZjckZlci1GJDYjLUknbXRhYmxlR0YlNiktSSRtdHJHRiU2Ki1JJG10ZEdGJTYjLUZkbzY5USI5RihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfby1GXHQ2Iy1GZG82OUZocUYzRjZGOUZnb0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuRmhvRl9vLUZcdDYjLUZkbzY5USI0RihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfby1GXHQ2Iy1GZG82OVEiMEYoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX28tRlx0NiMtRmRvNjlRIjJGKEYzRjZGOUZnb0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuRmhvRl9vLUZcdDYjLUZkbzY5USI4RihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZhdEZhdC1GaXM2KkZqdC1GXHQ2Iy1JJm1mcmFjR0YlNiotRmRvNjlRIzM0RihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZedC8lLmxpbmV0aGlja25lc3NHUSIxRigvJStkZW5vbWFsaWduR1EnY2VudGVyRigvJSludW1hbGlnbkdGaHYvJSliZXZlbGxlZEdGO0ZjckZlci1GXHQ2Iy1GXnY2Ki1GZG82OVEjMTlGKEYzRjZGOUZnb0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuRmhvRl9vRl50RmN2RmZ2Rml2Rlt3RmNyRmVyLUZcdEZiby1GXHQ2Iy1GXnY2Ki1GZG82OVEjMzJGKEYzRjZGOUZnb0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuRmhvRl9vRl50RmN2RmZ2Rml2Rlt3RmNyRmVyLUZcdDYjLUZedjYqLUZkbzY5USM0N0YoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GXnRGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NiotRmRvNjlRIzUyRihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZedEZjdkZmdkZpdkZbd0ZjckZlci1GXHQ2Iy1GXnY2Ki1GZG82OVEpJm1pbnVzOzJGKEYzRjZGOUZnb0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuRmhvRl9vRl50RmN2RmZ2Rml2Rlt3RmNyRmVyLUZpczYqRmp0Rmp0LUZcdDYjLUZedjYqLUZkbzY5USombWludXM7MThGKEYzRjZGOUZnb0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuRmhvRl9vLUZkbzY5USMxN0YoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NiotRmRvNjlRKiZtaW51czsyMkYoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GanlGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NiotRmRvNjlRKiZtaW51czsxNkYoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GanlGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NiotRmRvNjlRKiZtaW51czs2NkYoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GanlGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NipGZnVGanlGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NipGZ3hGanlGY3ZGZnZGaXZGW3dGY3JGZXItRmlzNipGanRGanQtRlx0NiMtRl52NiotRmRvNjlRKiZtaW51czszNkYoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GanlGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NiotRmRvNjlRIzc1RihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZqeUZjdkZmdkZpdkZbd0ZjckZlci1GXHQ2Iy1GXnY2KkZhdUZqeUZjdkZmdkZpdkZbd0ZjckZlci1GXHQ2Iy1GXnY2Ki1GZG82OVErJm1pbnVzOzE4M0YoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GanlGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NiotRmRvNjlRKSZtaW51czsxRihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZqeUZjdkZmdkZpdkZbd0ZjckZlci1GXHQ2Iy1GXnY2Ki1GZG82OVEjNzBGKEYzRjZGOUZnb0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuRmhvRl9vRmp5RmN2RmZ2Rml2Rlt3RmNyRmVyLUZpczYqRmp0Rmp0LUZcdDYjLUZedjYqLUZkbzY5USQxMTNGKEYzRjZGOUZnb0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuRmhvRl9vRmB2RmN2RmZ2Rml2Rlt3RmNyRmVyLUZcdDYjLUZedjYqLUZkbzY5USM4OUYoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GYHZGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NiotRmRvNjlRKiZtaW51czs0OEYoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GanlGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NiotRmRvNjlRKyZtaW51czszMTFGKEYzRjZGOUZnb0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuRmhvRl9vRmB2RmN2RmZ2Rml2Rlt3RmNyRmVyLUZcdDYjLUZedjYqLUZkbzY5USsmbWludXM7MTgwRihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZqeUZjdkZmdkZpdkZbd0ZjckZlci1GXHQ2Iy1GXnY2Ki1GZG82OVEkMTM5RihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZqeUZjdkZmdkZpdkZbd0ZjckZlci1GaXM2KkZqdEZqdC1GXHQ2Iy1GXnY2Ki1GZG82OVEqJm1pbnVzOzI5RihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZqeUZjdkZmdkZpdkZbd0ZjckZlci1GXHQ2Iy1GXnY2Ki1GZG82OVEqJm1pbnVzOzc3RihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZqeUZjdkZmdkZpdkZbd0ZjckZlci1GXHQ2Iy1GXnY2Ki1GZG82OVEqJm1pbnVzOzU2RihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZqeUZjdkZmdkZpdkZbd0ZjckZlci1GXHQ2Iy1GXnY2Ki1GZG82OVErJm1pbnVzOzI2NUYoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GanlGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NiotRmRvNjlRKyZtaW51czsxMDhGKEYzRjZGOUZnb0Y/RkFGQ0ZFRkhGS0ZNRk9GUUZTRlVGV0ZZRmZuRmhuRmpuRmhvRl9vRmp5RmN2RmZ2Rml2Rlt3RmNyRmVyLUZcdDYjLUZedjYqLUZkbzY5USM0NkYoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GanlGY3ZGZnZGaXZGW3dGY3JGZXItRmlzNipGanRGanQtRlx0NiMtRl52NiotRmRvNjlRKiZtaW51czs1N0YoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GanlGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NipGZ3RGanlGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NiotRmRvNjlRIzIzRihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZqeUZjdkZmdkZpdkZbd0ZjckZlci1GXHQ2Iy1GXnY2Ki1GZG82OVEqJm1pbnVzOzkwRihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZqeUZjdkZmdkZpdkZbd0ZjckZlci1GXHQ2Iy1GXnY2Ki1GZG82OVErJm1pbnVzOzE1NkYoRjNGNkY5RmdvRj9GQUZDRkVGSEZLRk1GT0ZRRlNGVUZXRllGZm5GaG5Gam5GaG9GX29GanlGY3ZGZnZGaXZGW3dGY3JGZXItRlx0NiMtRl52NiotRmRvNjlRIzU3RihGM0Y2RjlGZ29GP0ZBRkNGRUZIRktGTUZPRlFGU0ZVRldGWUZmbkZobkZqbkZob0Zfb0ZqeUZjdkZmdkZpdkZbd0ZjckZlci1GYHA2M1EiXUYoL0ZkcFEocG9zdGZpeEYoRl5zRmhwRl9zL0ZecVEydmVyeXRoaW5tYXRoc3BhY2VGKEZic0ZhcUZjcUZmcUZpcUZbckZdckZfckZhckZjckZlcjcjLV9GKUksbXByaW50c2xhc2hHRig2JDcjPiZJIk1HRig2IyIiJC1JJ1JUQUJMRUdGKDYlIigjZiF5Jy1JJ01BVFJJWEdGKDYjNyk3KiIiKiIiIiIiJSIiISIiIyIiKUZgaGxGYGhsNypGYmhsIyIjTUZfaGwjIiM+Rl9obEZlZ2wjIiNLRl9obCMiI1pGX2hsIyIjX0ZfaGwjISIjRl9obDcqRmJobEZiaGwjISM9IiM8IyEjQUZlaWwjISM7RmVpbCMhI21GZWlsI0ZkaGxGZWlsI0ZfaWxGZWlsNypGYmhsRmJobCMhI09GZWlsIyIjdkZlaWwjRmNobEZlaWwjISQkPUZlaWwjISIiRmVpbCMiI3FGZWlsNypGYmhsRmJobCMiJDgiRmdobCMiIyopRmdobCMhI1tGZWlsIyEkNiRGZ2hsIyEkIT1GZWlsIyIkUiJGZWlsNypGYmhsRmJobCMhI0hGZWlsIyEjeEZlaWwjISNjRmVpbCMhJGwjRmVpbCMhJDMiRmVpbCMiI1lGZWlsNypGYmhsRmJobCMhI2RGZWlsI0ZhaGxGZWlsIyIjQkZlaWwjISMhKkZlaWwjISRjIkZlaWwjIiNkRmVpbEknTWF0cml4RzYkJSpwcm90ZWN0ZWRHRio3Iy1GYF1tNiMvSSQlaWRHRihGaWds
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
Re-execute the section above many times.
Note 1 - If you try this with a matrix with a dimension greater than 10, Maple simply tells you it has a matrix rather than printing it out. The simplest way to see such a matrix is to double click it and to invoke the matrix browser. One can also change the size at which this happens can be shifted with an interface(rtablesize=n) command.
Note 2 - You should note that the algorithm fails if a zero shows up at the wrong spot. Test by example to see how often this happens. Decide if you want to modify the demo to eliminate this problem or if you want to incorporate this into your teaching.
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