Your approach is nice, but not enough of course. First, you need to construct a differential equation for your second question. Third question comes with the second one. The answer for your first question is included in this line:
Full solution may look like as follows:
A=[4 -5;-2 1];
[V,D]=eig(A)
syms x1(t) x2(t)
x0=[2.9;2.6];
eq1=diff(x1,t)==A(1,:)*[x1(t);x2(t)];
eq2=diff(x2,t)==A(2,:)*[x1(t);x2(t)];
solx=dsolve([eq1 eq2],[x1(0)==2.9 x2(0)==2.6]);
x1=solx.x1
x2=solx.x2
t=subs(t,0:0.1:1);
x1=subs(x1,t);
x2=subs(x2,t);
plot(t,x1,'o',t,x2,'-*')
Best Answer