111年 - 111 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#145408

科目：研究所、轉學考(插大)◆工程數學 | 年份：111年 | 選擇題數：0 | 申論題數：8

1. (a) Find the inverse Laplace transform of \( \frac{-2s+6}{s^2+4} \). (10%)

(b)請利用 Laplace 轉換技巧解微分方程式: y”-3y’+2y=e-4t ; y(0)=1, y’(0)=5 (20%) (未利用拉氏轉換解題，不予計分)

(a) Find the homogeneous solution y_ℎ (10%)

(b) Find the solution of the ODE (20%)

3. Solve (if possible) each of the following system of three equations in three variables using the method of Gauss-Jordan elimination. (20%)

\( \begin{cases} x_1 + 2x_2 - x_3 = 3 \\ 2x_1 + 4x_2 - 2x_3 = 6 \\ 3x_1 + 6x_2 + 2x_3 = -1 \end{cases} \)

(a) Show that the following matrix A is diagonalizable. (5%)

(b) Find a diagonal matrix D that is similar to A. (5%)