Determine the eigenvalues and eigenvectors for the following matrices:
a) [A] = [1,0,0; 0,7,0; 0,0,11]
b) [A] = [1,0,0; 0,3,1; 0,1,3]
c) [A] = [3,0,1; 0,1,0; 1,0,3]
d) [A] = [3,1,0; 1,3,0; 0,0,1]
Hint: in all these matrices at least one eigenvalue is lambda=1 Think about how the results of b) can be used to solve c) and d) I need a step by step answer to all parts of the question for points.