複選題

12. (10%) For the matrix A, which of the following are correct?
A =
(A) The rank of A is 4.
(B) The rank of A is 3.
(C) The dimension of null space of A is 0.
(D) The dimension of null space of A is 1.

(E) The dimension of null space of A is 2.

8. (5%) The initial value problem is described as follows: y" + 4y = 0； y(0) = 2, y'(0) = 2. The Laplace transform Y(s) of the solution y(t) is:(A)(B)(C) (D)(E)

9. (5%) The differential equation x" + 3x' - 5x = sin t is equivalent to the system:(A)x' = 3x - 5y； y' = sin t(B) x' = 5x - 3y； y' = sin t(C) x' = y； y' = 5x - 3y + sin t(D)x' = y； y' = 3x - 5y + sin t(E) None of above

複選題10. (5%) The differential equation is y' = in the standard form, and 2xydx + x²dy = 0 in a differential form. This differential equation is(A) linear(B) homogenous(C) exact(D) separable(E) Bernoulli

複選題11. (10%) Which of the following are correct?(A) The system defined by F(x,y)=(x², x) is linear.(B) The system defined by F(x,y)=(dx/dt, x) is linear.(C) A and B are m x n matrices. If Aw = Bw for all w in Rn, then A = B.(D) The columns of matrix A contains zero vector. If Ax=b have solution, it will have infinite solutions.(E) The zero vector of Rn is within the span of any finite subset of Rn.

複選題13. (5%) Which of the following are correct?(A) Below vector set S is dependent.S =(B) Invertible matrix must be square matrix.(C) Square matrix must be invertible.(D) The inverse of matrix(E) A n x n matrix is invertible if its columns span Rn.

複選題14. (10%) For the matrix below, which of the following are correct?(A) -1 is its eigenvalue.(B) 1 is its eigenvalue.(C) -3 is its eigenvalue.(D) Zero vector belongs to its eigenvector.(E) [1 0 2]T is a basis of its eigenspace.

複選題15. (5%) Which of the following are correct?(A) An eigenvalue of a matrix has infinite number of eigenvectors.(B) If det(A – λIn) = 0, λ is the eigenvalue of n x n matrix A.(C) If λ is the eigenvalue of matrix A, the columns of (A -λIn) are independent.(D) If λ is the eigenvalue of matrix A, there exist a non-zero vector v such that Av = λv.(E) The number of the eigenvalue of n x n matrix A may larger than n.

複選題16. (10%) Which of the following are correct?(A) Any orthogonal set of vectors is linearly independent.(B) Any orthonormal set of vectors is linearly independent.(C) If n x n matrix A is orthogonal, A is invertible.(D) If n x n matrix A is orthogonal, AAT=In.(E) If n x n matrix A is orthogonal, det( A ) = 1

1. 下列何者於道路上指揮攔阻人、車通行時,依道路交通管理處罰條例將受處新臺幣一千二百元以上二千四百元以下罰鍰 (A) 國中以下交通服務隊現場導護人員 (B) 高中以上交通服務隊現場導護人員 (C) 停車場管理員 (D) 以上皆是

2. 慢車及汽車駕駛人,行近行人穿越道遇有攜帶白手杖或導盲犬之視覺功能障礙者時,不暫停讓視覺功能障礙者先行通過者,分別處新臺幣多少罰緩 (A) 六百元以上一千二百元以下、一千二百元以上三千六百元以下 (B) 一千二百元以上二千四百元以下、二千四百元以上七千二百元以下 (C) 一千二百元以上三千六百元以下、三千六百元以上七千二百元以下 (D) 六百元以上一千二百元以下、二千四百元以上七千二百元以下