阿摩線上測驗 登入

最新科目

最新試卷

最新試題

25. (4 points) Which of the following statements are correct? (A) If Q is orthogonal, then det(Q) = = +1. (B) Let A be a real n x n matrix. Then A is symmetric if and only if A is orthogonally equivalent to a real diagonal matrix. (C) Let A E Rixm be a matrix whose characteristic polynomial splits over R. Then A is orthogonally equivalent to a real upper triangular matrix. (D) Let T be a self-adjoint (Hermitian) operator on a finite-dimensional inner product space V. Then every eigenvalue of T is positive. (E) Let T be a self-adjoint (Hermitian) operator on a finite-dimensional inner product space V. Then every eigenvalue of T is negative.

24. (4 points) Let Wi and Wa be subspaces of a finite-dimensional vector space V. Let 6 denote the direct sum. Which of the following statements are correct? (A) Win Wa is a subspace of V. (B) WiUW2 is a subspace of V. (C) W1+W2 is a subspace of V. (D) If V = Wi @ Wa, and Bi and Be are bases for Wi and Wa, respectively, then Bi O Bz = 0, and B1 U Bz is a basis for V. (E) If Wi e Wa = V, then the dimension dim(V) = dim(Wi)+dim(Wz).

23. (4 points) Which of the following statements are NOT correct? (A) If S is linearly independent and generates V, each vector in V can be expressed uniquely as a linear combination of vectors in S. (B) Every vector space has at least two distinct subspaces. (C) No vector is its own additive inverse. (D) All vector spaces having a basis are fnitely generated. (E) Any two bases in a finite-dimensional vector space V have the same number of elements.

最新申論題

最新課程

最新主題筆記

最新討論

9. 下列是有關改革後公文之敘述,請問何者正確? (A)公布法律及行政規章用「函」。 (B)政府機關向公眾宣布事項用「通知」。 (C)總統與立法院、監察院公文往復用「咨」。 (D)軍事機關下行公文,一律用「函」、「書函」行之。

20. 加拉巴哥群島不同雀鳥的鳥喙形態與功能之差異,推測是藉由食性所驅使的演化過程;而達爾文也藉由此一觀察與歸納提出「天擇說」來說明生物演化的可能原因。下列何種鳥喙形態所對應的食性是正確的? (A) 錐狀喙嗜食種子 (B) 針狀喙嗜食嫩芽 (C) 鸚嘴喙嗜食昆蟲 (D) 鉤叉喙嗜食花蜜

10. If you’ve ever cut your finger, bruised a toe or had a throat infection, you have likely experienced at least some of the four signs of _____: redness, swelling, pain and heat. (A) digestion (B) injection (C) inflammation (D) hydration

11. Preventative care, a routine _____ performed by a veterinarian, is the most effective method of stopping diseases before they occur. (A) surgery (B) checkup (C) infection (D) treatment

12. We find that the rivals' ability to threaten each other is a critical _____ of the outcome of bargaining. (A) determinant (B) consequence (C) hesitation (D) interruption

2. 有關RC暫態電路在放電期間,下列敘述何者有誤? (A)於充、放電時電路電流方向相反 (B)穩態時,電阻壓降等於電源電壓 (C)開關閉合瞬間,電容壓降等於電源電壓 (D)電路電流由大至小變化