Ch-6-Prob-6-New-이승진

2274 days ago by matrix

U=QQ^2 V=QQ^3 A=matrix(QQ,[[1,3],[2,6],[0,1]]) T=linear_transformation(U, V, A, side='right') print A.rref() print T.kernel() print "Is T injective? ", T.is_injective() print T.image() print "Is T surjective? ", T.is_surjective() 
        
[1 0]
[0 1]
[0 0]
Vector space of degree 2 and dimension 0 over Rational Field
Basis matrix:
[]
Is T injective?  True
Vector space of degree 3 and dimension 2 over Rational Field
Basis matrix:
[1 2 0]
[0 0 1]
Is T surjective?  False
[1 0]
[0 1]
[0 0]
Vector space of degree 2 and dimension 0 over Rational Field
Basis matrix:
[]
Is T injective?  True
Vector space of degree 3 and dimension 2 over Rational Field
Basis matrix:
[1 2 0]
[0 0 1]
Is T surjective?  False