11.令。方程式的平衡點發生在
(A)(y₁,y₂)= (0,0)
(B)(y₁,y₂)=(π,0)
(C) 以上皆是

複選題7. Let Pn denote the set of all polynomials of degree less than n. Which of the following statements are true? (A) Suppose V1, V2, V3 are linearly independent vectors in P3. Then V1, V2, V3 span P3. (B) If V1,V2, V3 are linearly dependent, then Span(v1, v2) must be equal to Span(v2, v3). (C) P2 is a subspace of P3. (D) Ifv1 + v2 + V3 equals the zero polynomial, then V1, V2, V3 must be linearly dependent. (E) If V1,V2, .., Vm span a vector space V, then V1, V2, ..., Vm must be linearly independent.

複選題8. Let and Let p be the orthogonal projection of b onto N( A ). Suppose b - p = av1 + βv2. Which of the following statements are true? (A)9a=8 (B) 9a= 9 (C) 9 β = 7 (D) 9 β=8 (E) 9a + 9 β = 15

複選題9.Define a mapping L: R3 →R3 by L(x) = Kx, where . Suppose that E = {p, Kp, K2p} is an ordered basis of R3, and K3p - 5K2p + 7Kp - 11p = 0. Let A be the matrix representation of L with respect to basis E. SupposeWhich of the following statements are true? (A) (B)(C) (D)(E)

複選題10. Let S be the transition matrix from {V1,V2} to {u1, u2}. Suppose Which of the following statements are true? (A)a=-1 (B)b= 2(C)c=3 (D)d=4 (E) a +b+c+d= 23

12.若μ＞0,則初值在平衡點(y1,y2)=(0,0)附近的解會隨時間增加而 (A)收斂到(0,0)(B)遠離(0,0)(C)不一定,跟初值有關。

13.若μ＜0,則初值在平衡點(y1,y2)=(0,0)附近的解會隨時間增加而 (A)收斂到(0,0)(B)遠離(0,0)(C)不一定,跟初值有關。

14.考慮對(y1,y2)=(π,0)作線性化之線性方程式此時,若μ＜0,則該線性方程式之非零初值 解會隨時間增加而 (A)收斂到(0,0)(B)遠離(0,0)(C)不一定,跟初值有關。

15.考慮上題所述之線性方程式此時,若μ＞0,則該線性方程式之非零初值解會隨時間增加而 (A)收斂到(0,0)(B)遠離(0,0)(C)不一定,跟初值有關。

 下面16-20题為單選題,每题1分,總分5分。答錯或未作答者該題以0分計 考慮函數(R代表實数所成之集合)及Laplace轉换,定義為: 以下第16题到20题,我們令F(s)=L(f(t))。16.請問Laplace轉换是否為一個線性操作? (A)是(B)否(C)不一定,與函數f有關。

17.等於以下哪個函數? (A)(B) sF(s)(C)以上兩者都不是。