If the determinant of A is zero A is not diagonalizable.
True
False
![If the determinant of A is zero A is not diagonaliza- ble. Ans: FALSE Examples: A= B [8]. det a = o, but A= 0, but A is diago](http://img.homeworklib.com/questions/ba2183b0-eb12-11ea-b8cc-7f4fb83536a3.png?x-oss-process=image/resize,w_560)
If A is singular then A is diagonalizable. True False
Indicate whether the statement is true or false: If a matrix is invertible and diagonalizable, then its inverse is diagonalizable O O True False
True or False: If A is an matrix that is both diagonalizable and invertible, then so is A-1. If true, briefly explain why; if false give a counterexample. Hint: consider taking the inverse of both sides of the equation A = PDP-1
Indicate whether the statements are true or false (a) If A is orthogonally diagonalizable, then so is A2 (b) For any matrix A e Rmxn, AAT and AT A are symmetric matrices
18. True or False? Culture is the fundamental determinant of a person's wants and behavior. Explain.
True or False? (a) An n x n matrix that is diagonalizable must be symmetric. (b) If AT = A and if vectors u and v satisfy Au = 3u and Av = 40, then u: v=0. (c) An n x n symmetric matrix has n distinct real eigenvalues. (d) For a nonzero v in R", the matrix vv7 is a rank-1 matrix.
True False a) For nxn A, A and AT can have different eigenvalues. b) The vector v 0 cannot be an eigenvector of A. c) If λ's an eigenvalue of A, then λ2 is an eigenvalue of A2. True False d) If A is invertible, then A is diagonalizable. e) If nxn A is singular, then Null(A) is an eigenspace of A. f) For nxn A, the product of the eigenvalues is the trace of A. True False g) If...
19. Population size is the most important determinant of effective sample size. A) True B) False 20. Pie charts are useful for depicting changes over time. A) True B) False 21. The median is always equal to the mean. A) True B) False 22. Data mining is a long-established field of market research. A) True B) False 23. Persuasion should never be used in the personal presentation of a marketing research report. A) True B) False _24. Clients tend to...
With explanation and examples
(a) True or False: If vy is an eigenvector of A with eigenvalue A, then v\ is also an eigenvector of A2 3-13. (b) True or False: If vx is an eigenvector of A with eigenvalue X and A is invertible, then va is also an eigenvector of A-1. (c) It is known that the product of the eigenvalues of a square matrix is the determinant of that matrix. True or False: A matrix with a...
Let A be an n×n matrix. Mark each statement as true or false. Justify each answer. a. An n×n determinant is defined by determinants of (n−1)×(n−1) submatrices. b. The (i,j)-cofactor of a matrix A is the matrix obtained by deleting from A its I’th row and j’th column. a. Choose the correct answer below. A. The statement is false. Although determinants of (n−1)×(n−1)submatrices can be used to find n×n determinants,they are not involved in the definition of n×n determinants. B....