110年 - 110 國立嘉義大學_碩士班招生考試試題_電機工程學系：工程數學#146536

1. y”+4y’+3y=et ; y(0)=0, y’(0)=2 (10%)
1+ω??

2. To inverse the Fourier transformation of (10%)
6−??2 +5ω??
??

3. To obtain f(t) when f(t)=2t2+∫0 ??(?? − α) ?? −α ??α (20%)

4. To obtain the Laplace transform of f(t) as shown below (20%)

5. To obtain the Fourier transformation of f(t)= ?? −??|??| (10%)

6. The following system of equations has unique solution. Solve the system using the method of
Gauss-Jordan elimination with matrix. (10%)
x1 − x2 + 3 x3 = 3
2 x1 − x2 + 2 x3 = 2
3 x1 + x2 − 2 x3 = 3

7. Determine the characteristic polynomial, eigenvalues, and corresponding eigenspaces of the
following matrix. (10%)
 5 −7 7
 4 −3 4

 4 − 1 2

8. We know that if D = C–1AC, then Ak = CDkC–1. Use this result to compute the following
power. (10%)
 1.5 − 0.5
16

− 0.5 1.5
