2) Let A be an n × n matrix and suppose that x and y are eigenvectors of A corresponding to the same eigenvalue of . Show that ax + By is also an eigenvector of A corresponding to the eigenvalue of 1...

ODE question

Extracted text: 2) Let A be an n × n matrix and suppose that x and y are eigenvectors of A corresponding to the same eigenvalue of . Show that ax + By is also an eigenvector of A corresponding to the eigenvalue of 1 for any real numbers a and ß.