Problem 1. ? ? ? ? ? Are the following statements true or false for a square matrix A? 1. A number c is an eigenvalue of A if and only if the equation (A − cI)x= 0 has a nontrivial solution X. 2. A matrix A is singular if and only if 0 is an eigenvalue of A. 3. To find the eigenvalues of A, reduce A to echelon form. 4. If Ax = 2x for some vector X and some scalar λ, then is an eigenvalue of A. 5. An n x n matrix A is diagonalizable if A has n linearly independent eigenvectors.

Problem 1. ? ? ? ? ? Are the following statements true or false for a square matrix A? 1. A number c is an eigenvalue of A if and only if the equation (A − cI)x= 0 has a nontrivial solution X. 2. A matrix A is singular if and only if 0 is an eigenvalue of A. 3. To find the eigenvalues of A, reduce A to echelon form. 4. If Ax = 2x for some vector X and some scalar λ, then is an eigenvalue of A. 5. An n x n matrix A is diagonalizable if A has n linearly independent eigenvectors.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 78E: Find all values of the angle for which the matrix A=[cossinsincos] has real eigenvalues. Interpret...

See similar textbooks