試題詳解

(5%) Which of the following are correct?
(A) An eigenvalue of a matrix has infinite number of eigenvectors.
(B) If det(A -λl_n) = O, λ is the eigenvalue of n x n matrix A.
(C) IfA is the cigenvalue of matrix A, the columns of (A - λIn) are independent.
(D) Ifa is the eigenvalue of matrix A, there exist a non-zero vector V such that Av = av.
(E) The number of the eigenvalue of n x n matrix A may larger than n.