27. is not a unique solution.
(A) True.
(B) False.

28. If ATA is not invertible, then the system has no solution. (A) True. (B) False.

29. A is not always in Col A.  (A) True. (B) False.

30. b - A is always in Nul AT.  (A) True. (B) False.

31. C always have n orthogonal eigenvectors. (A) True. (B) False.

32. C always have n distinct real eigenvalues. (A) True. (B) False. 

33. C has positive and negative eigenvalues but no zero eigenvalues. (A) True. (B) False.

34. C can always be decomposed into A AT, where A is a matrix. (A) True. (B) Falsc.

35. C is exactly positive definite. (A) True. (B) False. 

複選題36. Which of the following statements regarding the cost of methods for solving an n x n linear system Ax = b are true? (A) The cost of computing the LU factorization is generally proportional to n?. (B) The cost of backward substitution on a dense upper triangular matrix is generally proportional to n. (C) If a matrix A has no more than 3 non-zero entries per row, the cost of each iteration of the Jacobi method is proportional to n. (D) If a matrix A has no more than 3 non-zero entries per row, the cost of each iteration of the Jacobi method is proportional to n3. (E) None.

複選題37. Which of the following methods can be used for solving the system Ax = b, where A is a symmetric, diagonally dominant, square n x n matrix? (A) LU factorization with full pivoting. (B) System of normal equations. (C) Gauss-Seidel method. (D) Jacobi method. (E) None.

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