SAGE TERCERA UNIDAD

190 days ago by karencepeda@tecpabellon

#1 M = MatrixSpace(QQ,2,3) A = M([[6,5,2270],[5,4,1880]]) print "A" print A 
        
A
[   6    5 2270]
[   5    4 1880]
A
[   6    5 2270]
[   5    4 1880]
A.echelon_form () 
        
[  1   0 320]
[  0   1  70]
[  1   0 320]
[  0   1  70]
#2 M = MatrixSpace(QQ,3,4) A = M([[1,1,1,5],[250,500,1000,2500],[100,180,330,890]]) print "A" print A 
        
A
[   1    1    1    5]
[ 250  500 1000 2500]
[ 100  180  330  890]
A
[   1    1    1    5]
[ 250  500 1000 2500]
[ 100  180  330  890]
A.echelon_form () 
        
[1 0 0 2]
[0 1 0 2]
[0 0 1 1]
[1 0 0 2]
[0 1 0 2]
[0 0 1 1]
#3 M = MatrixSpace(QQ,3,4) A = M([[1,1,1,5],[250,500,1000,2500],[0.6,1.08,1.98,5.35]]) print "A" print A 
        
A
[     1      1      1      5]
[   250    500   1000   2500]
[   3/5  27/25  99/50 107/20]
A
[     1      1      1      5]
[   250    500   1000   2500]
[   3/5  27/25  99/50 107/20]
A.echelon_form () 
        
[  1   0   0 5/3]
[  0   1   0 5/2]
[  0   0   1 5/6]
[  1   0   0 5/3]
[  0   1   0 5/2]
[  0   0   1 5/6]
#4 M = MatrixSpace(QQ,3,4) A = M([[1,1,1,75.73],[1,-3,-3,0],[0,-0.18,-0.12,0]]) print "A" print A 
        
A
[       1        1        1 7573/100]
[       1       -3       -3        0]
[       0    -9/50    -3/25        0]
A
[       1        1        1 7573/100]
[       1       -3       -3        0]
[       0    -9/50    -3/25        0]
A.echelon_form () 
        
[        1         0         0 22719/400]
[        0         1         0 -7573/200]
[        0         0         1 22719/400]
[        1         0         0 22719/400]
[        0         1         0 -7573/200]
[        0         0         1 22719/400]
#5 M = MatrixSpace(QQ,3,4) A = M([[1,2,1,1.83],[2,3,2,3.03],[-2,0,1,0.57]]) print "A" print A 
        
A
[      1       2       1 183/100]
[      2       3       2 303/100]
[     -2       0       1  57/100]
A
[      1       2       1 183/100]
[      2       3       2 303/100]
[     -2       0       1  57/100]
A.echelon_form () 
        
[     1      0      0      0]
[     0      1      0 63/100]
[     0      0      1 57/100]
[     1      0      0      0]
[     0      1      0 63/100]
[     0      0      1 57/100]
#6 M = MatrixSpace(QQ,3,4) A = M([[1,1,1,60],[0,2,1,55],[1000,2000,4000,125000]]) print "A" print A 
        
A
[     1      1      1     60]
[     0      2      1     55]
[  1000   2000   4000 125000]
A
[     1      1      1     60]
[     0      2      1     55]
[  1000   2000   4000 125000]
A.echelon_form () 
        
[ 1  0  0 25]
[ 0  1  0 20]
[ 0  0  1 15]
[ 1  0  0 25]
[ 0  1  0 20]
[ 0  0  1 15]
#7 M = MatrixSpace(QQ,3,4) A = M([[1,1,1,110],[0,1,-1,19/18],[1,-1,0,6/5]]) print "A" print A 
        
A
[    1     1     1   110]
[    0     1    -1 19/18]
[    1    -1     0   6/5]
A
[    1     1     1   110]
[    0     1    -1 19/18]
[    1    -1     0   6/5]
A.echelon_form () 
        
[        1         0         0 10211/270]
[        0         1         0  9887/270]
[        0         0         1  4801/135]
[        1         0         0 10211/270]
[        0         1         0  9887/270]
[        0         0         1  4801/135]
#8 M = MatrixSpace (QQ,3,4) A = M([[1,1,1,60],[0,2,1,55],[6.01,12.02,24.04,751.25]]) print "A" print A 
        
A
[      1       1       1      60]
[      0       2       1      55]
[601/100  601/50  601/25  3005/4]
A
[      1       1       1      60]
[      0       2       1      55]
[601/100  601/50  601/25  3005/4]
A.echelon_form () 
        
[ 1  0  0 25]
[ 0  1  0 20]
[ 0  0  1 15]
[ 1  0  0 25]
[ 0  1  0 20]
[ 0  0  1 15]
#9 M = MatrixSpace (QQ,3,4) A = M([[1,1,1,20],[1,1,-3,0],[-1,1,0,-1]]) print "A" print A 
        
A
[ 1  1  1 20]
[ 1  1 -3  0]
[-1  1  0 -1]
A
[ 1  1  1 20]
[ 1  1 -3  0]
[-1  1  0 -1]
A.echelon_form () 
        
[1 0 0 8]
[0 1 0 7]
[0 0 1 5]
[1 0 0 8]
[0 1 0 7]
[0 0 1 5]
#10 M = MatrixSpace (QQ,2,3) A = M([[4,-3,10],[-3,2,7]]) A.echelon_form () 
        
[  1   0 -41]
[  0   1 -58]
[  1   0 -41]
[  0   1 -58]
(4*(-41)-3*(-58)) 
        
10
10
(-3*(-41)+2*(-58)) 
        
7
7
#11 M = MatrixSpace (QQ,3,4) A = M([[2,-1,1,-3],[-1,2,-2,3],[-3,2,2,1]]) A.echelon_form () 
        
[ 1  0  0 -1]
[ 0  1  0  0]
[ 0  0  1 -1]
[ 1  0  0 -1]
[ 0  1  0  0]
[ 0  0  1 -1]
(2*(-1)-(0)+(-1)) 
        
-3
-3
(-(-1)+2*(0)-2*(-1)) 
        
3
3
(-3*(-1)+2*(0)+2*(-1)) 
        
1
1
#12 M = MatrixSpace (QQ,2,3) A = M([[1,1,160],[1,-1,34]]) A.echelon_form () 
        
[ 1  0 97]
[ 0  1 63]
[ 1  0 97]
[ 0  1 63]
#13 M = MatrixSpace (QQ,3,4) A = M([[4,3,1,26],[2,2,2,26],[2,6,1,26]]) A.echelon_form () 
        
[1 0 0 3]
[0 1 0 2]
[0 0 1 8]
[1 0 0 3]
[0 1 0 2]
[0 0 1 8]
#14 M = MatrixSpace (QQ,2,3) A = M([[2,3,7.80],[5,4,13.2]]) A.echelon_form () 
        
[  1   0 6/5]
[  0   1 9/5]
[  1   0 6/5]
[  0   1 9/5]
#15 M = MatrixSpace (QQ,2,3) A = M([[1,1,45],[32,28,1368]]) A.echelon_form () 
        
[ 1  0 27]
[ 0  1 18]
[ 1  0 27]
[ 0  1 18]
#16 M = MatrixSpace (QQ,2,3) A = M([[1,1,29],[2,4,92]]) A.echelon_form () 
        
[ 1  0 12]
[ 0  1 17]
[ 1  0 12]
[ 0  1 17]
#17 M = MatrixSpace (QQ,2,3) A = M([[1,1,50],[1,-0.5,24.5]]) A.echelon_form () 
        
[ 1  0 33]
[ 0  1 17]
[ 1  0 33]
[ 0  1 17]
#18 M = MatrixSpace (QQ,2,3) A = M([[1,1,1100],[1.5,2,2000]]) A.echelon_form () 
        
[  1   0 400]
[  0   1 700]
[  1   0 400]
[  0   1 700]
#19 M = MatrixSpace (QQ,2,3) A = M([[1,1,154],[1/1,0,8/3]]) A.echelon_form () 
        
[    1     0   8/3]
[    0     1 454/3]
[    1     0   8/3]
[    0     1 454/3]
#20 M = MatrixSpace (QQ,2,3) A = M([[1,1,140],[1,2,14]]) A.echelon_form () 
        
[   1    0  266]
[   0    1 -126]
[   1    0  266]
[   0    1 -126]
#21 M = MatrixSpace (QQ,2,3) A = M([[1,1,70],[0.82,0.78,55.72]]) A.echelon_form () 
        
[ 1  0 28]
[ 0  1 42]
[ 1  0 28]
[ 0  1 42]
#22 M = MatrixSpace (QQ,2,3) A = M([[1,1,126],[1.14,0,0.75]]) A.echelon_form () 
        
[      1       0   25/38]
[      0       1 4763/38]
[      1       0   25/38]
[      0       1 4763/38]
#23 M = MatrixSpace (QQ,2,3) A = M([[1,1,420],[0.42,0.52,196]]) A.echelon_form () 
        
[  1   0 224]
[  0   1 196]
[  1   0 224]
[  0   1 196]
#24 M = MatrixSpace (QQ,2,3) A = M([[35,25,1220],[125.35,95.25,1390]]) A.echelon_form () 
        
[          1           0    16291/40]
[          0           1 -104277/200]
[          1           0    16291/40]
[          0           1 -104277/200]
#24 M = MatrixSpace (QQ,2,3) A = M([[1,1,50],[3.5,2,154]]) A.echelon_form () 
        
[ 1  0 36]
[ 0  1 14]
[ 1  0 36]
[ 0  1 14]
#25 M = MatrixSpace (QQ,2,3) A = M([[1,1,150],[50,15,5400]]) A.echelon_form () 
        
[ 1  0 90]
[ 0  1 60]
[ 1  0 90]
[ 0  1 60]
#26 M = MatrixSpace (QQ,3,3) A = M([[1,1,4],[1,-2,1],[2,6,0]]) A.echelon_form () 
        
[1 0 0]
[0 1 0]
[0 0 1]
[1 0 0]
[0 1 0]
[0 0 1]
#27 M = MatrixSpace (QQ,3,3) A = M([[1,-1,2],[2,-3,3],[1,1,5]]) A.echelon_form () 
        
[1 0 0]
[0 1 0]
[0 0 1]
[1 0 0]
[0 1 0]
[0 0 1]
#28 M = MatrixSpace (QQ,2,3) A = M([[-1,1,10],[1,2,-1]]) A.echelon_form () 
        
[ 1  0 -7]
[ 0  1  3]
[ 1  0 -7]
[ 0  1  3]
#29 M = MatrixSpace (QQ,2,3) A = M([[5,-1,22],[1,-1,10]]) A.echelon_form () 
        
[ 1  0  3]
[ 0  1 -7]
[ 1  0  3]
[ 0  1 -7]
#30 M = MatrixSpace (QQ,3,3) A = M([[1,-1,10],[5,-1,22],[1,2,1]]) A.echelon_form () 
        
[1 0 0]
[0 1 0]
[0 0 1]
[1 0 0]
[0 1 0]
[0 0 1]
#31 M = MatrixSpace (QQ,2,3) A = M([[1,1,0],[1,-1,2]]) A.echelon_form () 
        
[ 1  0  1]
[ 0  1 -1]
[ 1  0  1]
[ 0  1 -1]
#32 M = MatrixSpace (QQ,2,3) A = M([[1,1,0],[-1,7,16]]) A.echelon_form () 
        
[ 1  0 -2]
[ 0  1  2]
[ 1  0 -2]
[ 0  1  2]
#33 M = MatrixSpace (QQ,2,3) A = M([[1,-1,2],[-1,7,16]]) A.echelon_form () 
        
[1 0 5]
[0 1 3]
[1 0 5]
[0 1 3]
#34 M = MatrixSpace (QQ,2,3) A = M([[2,-3,1],[1,1,8]]) A.echelon_form () 
        
[1 0 5]
[0 1 3]
[1 0 5]
[0 1 3]
#35 M = MatrixSpace (QQ,2,3) A = M([[0.2,-1.7,6.1],[3,2,9]]) A.echelon_form () 
        
[ 1  0  5]
[ 0  1 -3]
[ 1  0  5]
[ 0  1 -3]
#36 M = MatrixSpace (QQ,2,3) A = M([[13,-8,15],[7,-14,9]]) A.echelon_form () 
        
[    1     0 23/21]
[    0     1 -2/21]
[    1     0 23/21]
[    0     1 -2/21]
#37 M = MatrixSpace (QQ,2,3) A = M([[9,-13,54],[11,-7,22]]) A.echelon_form () 
        
[     1      0 -23/20]
[     0      1 -99/20]
[     1      0 -23/20]
[     0      1 -99/20]
#38 M = MatrixSpace (QQ,2,3) A = M([[10,-15,62],[28,4,12]]) A.echelon_form () 
        
[       1        0  107/115]
[       0        1 -404/115]
[       1        0  107/115]
[       0        1 -404/115]