A student A is given the task of computing the eigenvalues of a n n matrix where n is atleast 106. He approaches his friend B for help. B says that the job is an extremely time-consuming one. A then says the matrix is an upper-triangular matrix. At this B says that he can obtain all the eigenvalues of the system by querying only n elements in the matrix. He claims to be able to solve for the eigenvalues of the system in O(n) time. Do you think B's confidence is justified? If so, what is the algorithm that B is going to use? If not, explain why B's confidence is misplaced.

(Subject reference is linear algebra)