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]]);

>