> | with(LinearAlgebra): |
54
> | A:=Matrix([[10,-53],[10,12]]); |
> | E:=Eigenvectors(A); |
> | M:=E[2]; |
> | C:=M^(-1).A.M; |
> | N:=1/2*Matrix([[1,-I],[1,I]]); |
> | M2:=M.N; |
> | C2:=M2^(-1).A.M2; |
> | C2E:=exp(11*t)*Matrix([[cos(23*t),sin(23*t)],[-sin(23*t),cos(23*t)]]); |
> | AE:=M2.C2E.M2^(-1); |
> | AE.Matrix([[23],[23]]); |
> |
> |
56
> | A:=Matrix([[-9,108,-92],[10,-90,79],[12,-124,107]]); |
> | E:=Eigenvectors(A); |
> | M:=E[2]; |
> | N:=Matrix([[1/2,-1/2*I,0],[1/2,1/2*I,0],[0,0,1]]); |
> | M2:=M.N; |
> | C:=M2^(-1).A.M2; |
> | CE:=Matrix([[exp(2*t),0,0],[0,exp(3*t)*cos(4*t),exp(3*t)*sin(4*t)],[0,-exp(3*t)*sin(4*t),exp(3*t)*cos(4*t)]]); |
> | AE:=M2.CE.M2^(-1); |
> |
> |
57
> | A:=Matrix([[-723,280,2744],[-91,40,343],[-182,70,691]]); |
> | g:=Matrix([[exp(5*t)],[3*t+7],[20]]); |
> | E:=Eigenvectors(A); |
> | M:=E[2]; |
> | C:=M^(-1).A.M; |
> | h:=M^(-1).g; |
> | s1:=solve(dsolve(diff(x(t),t)=5*x(t)+h[1,1]),x(t)); |
> | s2:=solve(dsolve(diff(x(t),t)=5*x(t)+h[2,1]),x(t)); |
> | s3:=solve(dsolve(diff(x(t),t)=-2*x(t)+h[3,1]),x(t)); |
> | y:=Matrix([[s1],[subs(_C1=c2,s2)],[subs(_C1=c3,s3)]]); |
> | M.y; |
> |
58
> | A:=Matrix([[1,3,0,0,0,0,-1,0],[0,18,-5,0,6,-25,0,-2],[0,64,-18,0,24,-100,0,-8],[-2,6,0,2,0,-1,-2,0],[0,116,-34,0,43,-170,0,-14],[0,0,0,0,0,2,0,0],[0,45,-13,0,15,-65,1,-5],[0,322,-94,0,114,-470,0,-37]]); |
> | M:=JordanForm(A,output='Q'); |
> | J:=M^(-1).A.M; |
> | Je:=MatrixExponential(J*t); |
> | Ae:=M.Je.M^(-1); |
> | Ae.Matrix([[1],[0],[1],[0],[0],[0],[0],[0]]); |
> |