8. (5%) Which is the general solution of the differential equation (assume C and G, are constants)
(A)
(B)
(C)
(D)
(E)

複選題9. (5%) Which are the possible solutions of function f(t) for the Laplace Transform (A) f= cosh(πt) (B) f- sinh(πt) (C) (D) (E)

10. (5%) Which are the possible solutions of system of equations for x(t) and y(t), where y(0) = 1 and = 1? (A)(B) (C) (D) (E)

11. (10%) Let Q be an n x n matrix. Then which of the following set is not a subspace? (A) ColQ (B) Null Q (C) rank Q (D) Row Q (E) None of the above

12. (10%) Let M be a subset of R' containing two or more vectors. Then: (A) The span of any two vectors in M is a plane in R3 (B) Every vector in M is in the span of M (C) If M contains more than three vectors, then M is linearly independent (D) The span of any two nonzero vectors in M is a plane in R3 (E) None of the preceding statements is true

13. (10%) Which of the following statements is true for all n x n matrices O? (A) @ has n distinct eigenvalues (B) If one of the eigenvalues of Q has multiplicity greater than one, then Q has fewer then n eigenvalues (C) If Q has no cigenvalues, then the degree of its characteristic polynomial is zero (D) If one of the eigenvalues of Q has multiplicity greater than one, then Q has fewer than n eigenvectors (E) None of the preceding statements are true

14. (10%) Suppose that s, t, and u are vectors in G" such that s is orthogonal to u and u is orthogonal to t. Then (A) For any orthogonal n x n matrix G, we have that Gs is orthogonal to u (B) For any orthogonal n x n matrix G, we have that Gu is orthogonal to both s and t (C)s is orthogonal to t (D) s + t is orthogonal to u (E) None of the preceding statements are true [cos(t)

複選題15. (10%) An m x n matrix Xis invertible if (A) The columns of X span Rm (B) The reduced row echelon form of X is In (C) The rows of X are linearly independent (D) The columns of X are linearly independent (E) None of the preceding statements is true

1. 將 4 庫侖之電荷由 X 點移至 Y 點，需作功 12 焦耳，則 X 與 Y 點間之電位差為幾伏特？ (A) 2V (B) 3V (C) 4V (D) 5V。

2. 1000 瓦特約等於多少馬力 hp？ (A) 4/5 (B) 3/4 (C) 2/3 (D) 4/3。

3. 若將導線的線徑和長度增加為原來的 2 倍，則電阻變成原來的？ (A) 0.5 倍 (B) 1 倍 (C) 2 倍 (D) 4 倍。

110年 - [非官方正解]110 國立臺灣大學_碩士班招生考試_部分系所:工程數學(C)(含微分方程、線性代數)#102900

109年 - [非官方正解]109 國立臺灣大學_碩士班招生考試_電機工程研究所甲、乙組:工程數學(C)(含微分方程、線性代數)#105836