Homework Questions

Can an eigenvalue be O? If a matrix is diagonalizable, then it must be invertible? O Yes True O No O False Can an eigenvector be a zero vector ? O Yes (Converse of spectral theorem) If a matrix A has a spectral decomposition i.e. A = QDQT for some orthogonal matrix Q and diagonal matrix D, then A must be symmetric? O No Let A = (8 3 ). which of the following value is not an eigenvalue of A ? O True O False O 1 O 2 Suppose a 2x2 matrix A has two eigenvalues dy and 12. If we know det(A) = 6 and )1 = 2, then what is the value of 12? At most how many distinct eigenvalues can a 5x5 matrix have? If a d x d matrix is diagonalizable, then it must have d distinct eigenvalues? O True O False