Question

1. Suppose that 4 and -1 are the only eigenvalues of a 2 x 2 matrix A. Which one of the following statements is true? A) 41 - A is invertible, and there is a nontrivial solution to Av = -v. B) 41 - A is not invertible, and there is a nontrivial solution to Av = v. C) det(41+ A) = det(-I + A) = 0. (D) det(41 - A) = 0 and rank(A + 1) = 1. E) None of the above.