# LA+CH6+Prob7+solved by 주민규

## 2459 days ago by jumin1046

x1,x2,x3,x4,x5=var('x1 x2 x3 x4 x5') SM_T1(x1,x2,x3,x4,x5)=(4*x1,x2-2*x1-3*x5,5*x3-4*x5-x1-3*x2,2*x4-x1-3*x2,4*x4-5*x5) SM_T2(x1,x2,x3,x4,x5)=(x1+2*x2-5*x5, (-1)*x3,x2,4*x1-3*x3+4*x4,-2*x2+5*x5) T1=linear_transformation(QQ^5, QQ^5,SM_T1) T2=linear_transformation(QQ^5, QQ^5,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
 [T1] = [ 4 0 0 0 0] [-2 1 0 0 -3] [-1 -3 5 0 -4] [-1 -3 0 2 0] [ 0 0 0 4 -5] [T2] = [ 1 2 0 0 -5] [ 0 0 -1 0 0] [ 0 1 0 0 0] [ 4 0 -3 4 0] [ 0 -2 0 0 5] [T2*T1] = [ 0 2 0 -20 19] [ 1 3 -5 0 4] [ -2 1 0 0 -3] [ 15 -3 -15 8 12] [ 4 -2 0 20 -19] [T1*T2]= [ 4 8 0 0 -20] [ -2 2 -1 0 -5] [ -1 11 3 0 -15] [ 7 -2 -3 8 5] [ 16 10 -12 16 -25] [T1] = [ 4 0 0 0 0] [-2 1 0 0 -3] [-1 -3 5 0 -4] [-1 -3 0 2 0] [ 0 0 0 4 -5] [T2] = [ 1 2 0 0 -5] [ 0 0 -1 0 0] [ 0 1 0 0 0] [ 4 0 -3 4 0] [ 0 -2 0 0 5] [T2*T1] = [ 0 2 0 -20 19] [ 1 3 -5 0 4] [ -2 1 0 0 -3] [ 15 -3 -15 8 12] [ 4 -2 0 20 -19] [T1*T2]= [ 4 8 0 0 -20] [ -2 2 -1 0 -5] [ -1 11 3 0 -15] [ 7 -2 -3 8 5] [ 16 10 -12 16 -25]