Therefore:
(a) .9 and .7 0 is an asymptotically stable state (b) 1.1 and .4 0 is NOT an asymptotically stable state (c) .5 +/- .4i 0 is an asymptotically stable state, since the eigenvalues have absolute value (.25 + .16)^{1/2} which is < 1.2. By definition, the matrix is
2 4 3 -5(Giving the transpose of this instead cost 2 points.)
3. The matrix with respect to the basis of columns of S is S^{-1} A S which is the product
-2 1 4 4 1 9 1 2 3 3 -2 -5 7 2 5 -1 0 2 -1 1 2 3 6 0 1 1 1(Reversing the roles of S^{-1} and S cost 2 points.)