LA+Chapter8+Ex+3(new)-서승완

2033 days ago by math2013

x, y, z = var('x, y, z') h(x, y, z) = [-x-6*z,3*x+4*z,-2*x+5*y] T = linear_transformation(QQ^3, QQ^3, h) x1=vector([1,0,0]) x2=vector([0,0,1]) x3=vector([1,1,0]) y1=vector([2,0]) y2=vector([0,1]) B=column_matrix([x1, x2, x3, T(x1), T(x2), T(x3)]) print B print C=B.echelon_form() print C print A=C.submatrix(0, 3, 3, 3) print A print P=matrix(3,3,[0,-3,3,-1,3,2,0,1,-3]) print P print P1=P.inverse() print P1 print print P1*A*P 
       
[ 1  0  1 -1 -6 -1]
[ 0  0  1  3  4  3]
[ 0  1  0 -2  0  3]

[  1   0   0  -4 -10  -4]
[  0   1   0  -2   0   3]
[  0   0   1   3   4   3]

[ -4 -10  -4]
[ -2   0   3]
[  3   4   3]

[ 0 -3  3]
[-1  3  2]
[ 0  1 -3]

[-11/6    -1  -5/2]
[ -1/2     0  -1/2]
[ -1/6     0  -1/2]

[-25/3  49/3  95/3]
[   -3     8     6]
[  1/3   2/3  -2/3]
[ 1  0  1 -1 -6 -1]
[ 0  0  1  3  4  3]
[ 0  1  0 -2  0  3]

[  1   0   0  -4 -10  -4]
[  0   1   0  -2   0   3]
[  0   0   1   3   4   3]

[ -4 -10  -4]
[ -2   0   3]
[  3   4   3]

[ 0 -3  3]
[-1  3  2]
[ 0  1 -3]

[-11/6    -1  -5/2]
[ -1/2     0  -1/2]
[ -1/6     0  -1/2]

[-25/3  49/3  95/3]
[   -3     8     6]
[  1/3   2/3  -2/3]