Page 425 - Schaum's Outline of Theory and Problems of Signals and Systems

412 STATE SPACE ANALYSIS [CHAP. 7

Eq. (7.33) we have

Then, by Eq. (7.70) we obtain

7.44. Given matrix

(a) Show that A is nilpotent of index 3.
(6) Using the result from part (a) find eA'.
(a) By direct multiplication we have

Thus, A is nilpotent of index 3.
(b) By definition (7.53) and the result from part (a)

7.45. Find eA' for matrix A in Prob. 7.44 using the Cayley-Hamilton theorem method.

First, we find the characteristic polynomial c(A) of A.
A 2 -
c(A)=lAl-A, =I0 A -il=A3
0 0