Final answer:
To determine the poles and invariant zeros of a state space system, we need to find the eigenvalues of the system's matrix. The eigenvalues are the poles, and the zeros can be found by setting the numerator of the transfer function equal to zero.
Step-by-step explanation:
The poles and invariant zeros of a state space system can be determined by finding the values of the system's transfer function that make the denominator equal to zero. In this case, the state space system is represented by the matrix [-1 -2 1] [0 2 -1] [-4 -3 2]. To find the poles, we need to find the eigenvalues of the matrix. The eigenvalues are the values of s that satisfy the equation |A - sI| = 0, where A is the matrix, and I is the identity matrix. The invariant zeros can be found by setting the numerator of the transfer function equal to zero.