Ch-8-Prob-2-New-황성빈

1850 days ago by matrix

x,y,z=var('x,y,z') a(x,y,z)=[x-2*y,5*x-y,2*x+3*y,3*y+4*z] T=linear_transformation(QQ^3,QQ^4,a) x1=vector([1,0,0]) x2=vector([1,0,0]) x3=vector([0,0,1]) y1=([1,0,0,0]) y2=([0,1,0,0]) y3=([0,0,1,0]) y4=([0,0,0,1]) B=column_matrix([y1,y2,y3,y4,T(x1),T(x2),T(x3)]) print B 
       
[1 0 0 0 1 1 0]
[0 1 0 0 5 5 0]
[0 0 1 0 2 2 0]
[0 0 0 1 0 0 4]
[1 0 0 0 1 1 0]
[0 1 0 0 5 5 0]
[0 0 1 0 2 2 0]
[0 0 0 1 0 0 4]
C=B.echelon_form() print C 
       
[1 0 0 0 1 1 0]
[0 1 0 0 5 5 0]
[0 0 1 0 2 2 0]
[0 0 0 1 0 0 4]
[1 0 0 0 1 1 0]
[0 1 0 0 5 5 0]
[0 0 1 0 2 2 0]
[0 0 0 1 0 0 4]
A=C.submatrix(0,4,4,3) print A 
       
[1 1 0]
[5 5 0]
[2 2 0]
[0 0 4]
[1 1 0]
[5 5 0]
[2 2 0]
[0 0 4]