x1,x2,x3=var('x1 x2 x3')
SM_T1(x1,x2,x3)=(5*x1-2*x2,-4*x1+3*x2+8*x3,6*x1-2*x2)
SM_T2(x1,x2,x3)=(3*x1+2*x3,2*x3,x1+3*x2-3*x3)
T1=linear_transformation(QQ^3, QQ^3,SM_T1)
T2=linear_transformation(QQ^3, QQ^3,SM_T2)
M_T1 = T1.matrix(side='right')
M_T2 = T2.matrix(side='right')
print "[T1] = \n",M_T1
print "[T2] = \n",M_T2
print "[T2*T1] = \n",M_T2*M_T1
print "[T1*T2]= \n",M_T1*M_T2
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[T1] =
[ 5 -2 0]
[-4 3 8]
[ 6 -2 0]
[T2] =
[ 3 0 2]
[ 0 0 2]
[ 1 3 -3]
[T2*T1] =
[ 27 -10 0]
[ 12 -4 0]
[-25 13 24]
[T1*T2]=
[ 15 0 6]
[ -4 24 -26]
[ 18 0 8]
[T1] =
[ 5 -2 0]
[-4 3 8]
[ 6 -2 0]
[T2] =
[ 3 0 2]
[ 0 0 2]
[ 1 3 -3]
[T2*T1] =
[ 27 -10 0]
[ 12 -4 0]
[-25 13 24]
[T1*T2]=
[ 15 0 6]
[ -4 24 -26]
[ 18 0 8]
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