Please answer the following matrix question In each part com

Please answer the following matrix question.

In each part, computer the matrix exponential e^At and solve the differential equation x\'(t) = Ax(t) with the initial condition x(0) = c, for the given vector c. (The expressions may get large, simplify when possible.) > A:= Matrix(4, 4, {(1, 1) = -418, (1, 2) = 189, (1, 3) = -1764, (1, 4) = -420, (2, 1) = 180, (2, 2) = -79, (2, 3) = 756, (2, 4) = 180, (3, 1) = 100, (3, 2) = -45, (3, 3) = 422, (3, 4) = 100, (4, 1) = 80, (4, 2) = -36, (4, 3) = 336, (4, 4) = 82}); A:= [-418 189 -1764 -420 180 -79 756 180 100 -45 422 100 80 -36 336 82] > c:=; c:= [-1 2 0 3] > A:= Matrix(4, 4, {(1, 1) = 75, (1, 2) = -14, (1, 3) = 9, (1, 4) = 9, (2, 1) = 365, (2, 2) = -68, (2, 3) = 45, (2, 4) = 45, (3, 1) = -297, (3, 2) = 57, (3, 3) = -26, (3, 4) = -27, (4, 1) = 271, (4, 2) = -52, (4, 3) = 25, (4, 4) = 26}); A:= [75 -14 9 9 365 -68 45 45 -297 57 -26 -27 271 -52 25 26] > c:=; c:= [1 2 -4 3]

Solution

A=[-418 189 -1764 -420;180 -79 756 180;100 -45 422 100;80 -36 336 82];
c=[-1; 2; 0; 3];
syms y(t),t;
>> y(t)=expm(A*t);%%calculates the matrix exponential%%
B=linsolve(x(0),c);

B*y(t)%% x(t)%%

ans =

462*exp(t) - 463*exp(2*t)
200*exp(2*t) - 198*exp(t)
110*exp(2*t) - 110*exp(t)
91*exp(2*t) - 88*exp(t)

A=[75 -14 9 9;365 -68 45 45;-297 57 -26 -27;271 -52 25 26];
c=[1; 2; -4; 3];
syms y(t),t;
x(t)=expm(A*t);
B=linsolve(y(0),c);
>> y(t)*B

ans =

exp(2*t) + 36*t*exp(2*t) - (9*t^2*exp(2*t))/2
2*exp(2*t) + 180*t*exp(2*t) - (45*t^2*exp(2*t))/2
44*exp(t) - 48*exp(2*t) - 108*t*exp(2*t) + (27*t^2*exp(2*t))/2
47*exp(2*t) - 44*exp(t) + 95*t*exp(2*t) - 12*t^2*exp(2*t)