所屬科目：研究所、轉學考(插大)◆工程數學
1. (5%) Which are the possible solutions of the differential equation =y2ー9? (A) y=3 (B) y=-3 (C) (D) (E)
2. (5%) Which are the possible solutions of the differential equatio? (A) (B)(C) (D) (E)
4. (5%) Consider the equationwith the boundary conditions y(0)=0,y(π)=π.Which dr dx statements are correct? (A) The particular solution is (B) The general solution is (C) There is a unique solution to this boundary-value problem. (D) This differential equation is homogencous. (E) None of the above.
5. (5%) Which are the possible solutions of the differential equation ? (A) y+ln|y-1|=x (B) 2y+1nly-1|=4x (C) 2y+1n|2y-1|=4x+4 (D) y2=2x (E) y2=-2x+1
6. (5%) Assume, Which statements are always true? (A) C0=0 (B) C1=0 (C)C2 =0 (D)(E)
7. (5%) Consider the equation with the inial condition y(0) =1. Which statemenas about the function y(t) and its Laplace transform Y(s) are correct? (A) (B) (C) y(t)=sint-tsint (D) y(π)=0 (E) y(π)=-1
8. (5%) Which are the possible solutions of the given system? (A)(B)(C)(D)
9. (5%) Consider the wave equation with initial conditions Which are the possible solutions? (A)u(x,r)=f(x-at) (B) u(x,t)=f(x+at) (C)(D) (E) None of the above
10.Ealuate the Fourier transfom (A) (B) (C) (D)(E)
11. (5%) Find an equation involving g, h, and k that makes this augmented matrix correspond to a consistent system:(A) 2k+g+h -0 (B) k+2g+3h =0 (C) k+2g+h = 0 (D) 3k+g+2h = 0
12.(5%) Let a1=. For what value(s) ofh is b in the plane
spanned by a1 and a2?
(A) 0
(B) -10
(C) 16
(E) 20
(D) -17
13. (5%) Determine the rank of the matrix in the following. (A)0 (B) 1 (C)2 (D)3 (E) 4
14. (5%) Matrix A can be written in the form A=LU, where L is m x m lower triangular matrix I's on the diagonal and U is an m x n echelon form of A. Such a factorization is called an LU factorization. Please find the L matrix for LU factorization of the following matrix A. (A)(B)(C)(D)(E)
15. (5%) Find the determinant for the following matrix. (A)-5 (B) 5 (C)1 (D)-1 (E) 0
16. (5%) Find the dimension of the subspace H = (A) 2 (B) 3 (C) 4 (D) 1 (E)0
17.Let Let , and consider the bases for R2 given by B ={b1,b2} and C={c1,c2}.Find the change-of-coordinates matrix from C to B.(A)(B)(C)(D)(E)
18. (5%) Which of the following statement is True? (A) If A is a 3 ✖ 3 matrix, then det 5A=5 det A. (B) If A3=0 ,then det A =0. (C) Ifu and v are in R2 and det[ u v]=10, then the area of the triangle in the plane with verices a at 0, u, v is 10. (D) IfA isn xn and det A=2, then det A3=6 . (E) Any system ofn linear equations in n variables can be solved by Cramer's rule.
19. (5%) Find the singular values of the following matrix. (A) 0 (B) 1 (C) 2 (D) 3 (E) 4
阿摩線上測驗
登入
阿摩線上測驗
登入
=y2ー9? (A) y=3 (B) y=-3 (C) 
(D) 
(E) 
? (A)
(B)
(C)
(D) 
(E) 
with the boundary conditions y(0)=0,y(π)=π.Which dr dx statements are correct? (A) The particular solution is
(B) The general solution is 
(C) There is a unique solution to this boundary-value problem. (D) This differential equation is homogencous. (E) None of the above.
? (A) y+ln|y-1|=x (B) 2y+1nly-1|=4x (C) 2y+1n|2y-1|=4x+4 (D) y2=2x (E) y2=-2x+1
, Which statements are always true? (A) C0=0 (B) C1=0 (C)C
(E) 
with the inial condition y(0) =1. Which statemenas about the function y(t) and its Laplace transform Y(s) are correct? (A) 
(B) 
(C) y(t)=sint-
tsint (D) y(π)=0 (E) y(π)=-1
(A)
(B)
(C)
(D)
with initial conditions
Which are the possible solutions? (A)u(x,r)=f(x-at) (B) u(x,t)=f(x+at) (C)
(D)
(E) None of the above
(A) 
(B)
(C) 
(D)
(E)
(A) 2k+g+h -0 (B) k+2g+3h =0 (C) k+2g+h = 0 (D) 3k+g+2h = 0 
. For what value(s) ofh is b in the plane
(A)0 (B) 1 (C)2 (D)3 (E) 4
(A)
(B)
(C)
(D)
(E)
. (A)-5 (B) 5 (C)1 (D)-1 (E) 0
(A) 2 (B) 3 (C) 4 (D) 1 (E)0
, and consider the bases for R2 given by B ={b1,b2} and C={c1,c2}.Find the change-of-coordinates matrix from C to B.(A)
(B)
(C)
(D)
(E)
. (A) 0 (B) 1 (C) 2 (D) 3 (E) 4