Let the affine transformation:
T(x)=Ax+b
Where A is nxn matrix and b is vector in Rn. Assume that 1 is not eigenvalue of A.
i) Determine vector v in Rn s.t. T(v)=v; this vector is known as equilbrum state of dynamical system x(t+1)=T(x(t))
b. When is equilibrium in part a) stable (lim as x-> infinity of x(t)=v for all trajectories)?