Question

A system has a state-space representation i (7 %)*+(i)" y = (1 1). Determine the eigenvalues, X1 and 12, and the corresponding eigenvectors, 01 and U2, of the system matrix A

Answer 1

The eigenvalues of the system matrix A are 7% and -7%, and the corresponding eigenvectors are (1 1) and (-1 1).

Step-by-step explanation:

The given system has a state-space representation of i(7%) * +(i)y = (1 1).

To determine the eigenvalues and eigenvectors of the system matrix A, we need to find the roots of the characteristic equation det(A - λI) = 0, where A is the matrix, λ is the eigenvalue, and I is the identity matrix.

Substituting the given matrix A = (7%)+ (i) into the characteristic equation and solving, we get the eigenvalues λ1 = 7% and λ2 = -7%. The corresponding eigenvectors are v1 = (1 1) and v2 = (-1 1).