?If A is invertible and 1 is an eigenvalue for A, then 1 is also an eigenvalue for A-1,?If A is row equivalent to the identity matrix I, then A is diagonalizable.

If A contains a row or column of zeros. then 0 is an eigenvalue of A. Each eigenvalue of A is also an eigenvalue of A2. Each eigenvalue of A is not an eigenvalue of A3. P'P'PF" Each eigenvector of A is also an eigenvector of A2. 7. Each eigenvector of an intervible matrix A is also an eigenvector of A'l. 8. Eigenvalues must be nonzero scalars. 9. Eigenvectors must be nonzero vectors. 10.Two eigenvectors corresponding to the same eigenvalue are always linearly dependent 11.Similar matrices always have exactly the same eigenvalues. 12. Similar matrices always have exactly the same elgenvectors. 13. The sum of Mo eigenvectors of a matrix A is also an eigenvector of A. 14.The eigenvalues of an upper triangular matrix A are exactly the nonzero entries on the diagonal of A. Copyright 2022 Post University, ALL RIGHTS RESERVED 15.The matrices A and AT have the same eigenvalues, counting multiplicities. 16.The matrices A and AT have the same eigenvectors. 17. If a 5 x 5 matrix A has fewer than 5 distinct eigenvalues. then A is not diagonalizable. 18.There exists a 2 x 2 matrix that has no eigenvectors in R2. 19. If A is diagonlizable. then the columns of A are linearly Independent. 20A nonzero vector cannot correspond to two different eigenvalues of A. 21 .A square matrix A is invertible if and only it there is a coordinate system in which the transformation x -> Ax. 22. If each vector 2} in the standard basis for 1R"- is an eigenvector of A. then A is a diagonal matrix. 23. If A is similar to a diagonelizable matrix B, then A is also diagonalizable. 24. If A and B are invertible n. x n matrices. then AB is similarto BA. 25.An n x 11 matrix with n linearly independent eigenvectors is invertible. 28. If A is an 'n. x w. diagonalizable matrix, then each vector in litn can be written as a linear combination of eigenvectors of A