Assume that A(t) is a 2x2 matrix with real, distinct eigenvalues, lam1 < lam2.
Let B denote the set of 2x2 matrices with eigenvalues of negative real part such that xBx > 0 for some x in R2. Prove that if ||x(t)|| --> infinity as t --> infinity, then A(t) in B for some t > 0.
I'm not sure where to start with this one. Any help would be greatly appreciated!