LA.Ch8.Ex1.NEW.SC.Kim

2030 days ago by seongchan

x1, x2, x3, x4 = var('x1, x2, x3, x4') f(x1, x2, x3, x4) = [x1-x2, x3-2*x2, x3+3*x4, x4-4*x1] T = linear_transformation(QQ^4, QQ^4, f) v1=vector([1, 0, 2, -1]) v2=vector([1, 1, -4, 0]) v3=vector([0, -1, 2, 3]) v4=vector([-2, 4, 1, 3]) A=column_matrix([v1, v2, v3, v4, T(v1), T(v2), T(v3), T(v4)]) print A print B=A.echelon_form() print B print C=B.submatrix(0, 4, 4, 4) print C 
       
[ 1  1  0 -2  1  0  1 -6]
[ 0  1 -1  4  2 -6  4 -7]
[ 2 -4  2  1 -1 -4 11 10]
[-1  0  3  3 -5 -4  3 11]

[       1        0        0        0  115/104  -113/52  381/104  
-47/13]
[       0        1        0        0      1/8     -3/4     -1/8      
-3]
[       0        0        1        0 -147/104   -31/52   99/104   
36/13]
[       0        0        0        1     3/26   -19/13    33/26   
-4/13]

[ 115/104  -113/52  381/104   -47/13]
[     1/8     -3/4     -1/8       -3]
[-147/104   -31/52   99/104    36/13]
[    3/26   -19/13    33/26    -4/13]
[ 1  1  0 -2  1  0  1 -6]
[ 0  1 -1  4  2 -6  4 -7]
[ 2 -4  2  1 -1 -4 11 10]
[-1  0  3  3 -5 -4  3 11]

[       1        0        0        0  115/104  -113/52  381/104   -47/13]
[       0        1        0        0      1/8     -3/4     -1/8       -3]
[       0        0        1        0 -147/104   -31/52   99/104    36/13]
[       0        0        0        1     3/26   -19/13    33/26    -4/13]

[ 115/104  -113/52  381/104   -47/13]
[     1/8     -3/4     -1/8       -3]
[-147/104   -31/52   99/104    36/13]
[    3/26   -19/13    33/26    -4/13]