We consider the real matrix
a) Determine
for n = 1 , 2 , 3 , 4 {\displaystyle {}n=1,2,3,4} .
b) Let
Establish a relation between the sequences x n {\displaystyle {}x_{n}} and y n {\displaystyle {}y_{n}} , and determine a recursive formula for these sequences.
c) Determine the eigenvalues and the eigenvectors of M {\displaystyle {}M} .