113年 - 113 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#144102

科目：研究所、轉學考(插大)◆工程數學 | 年份：113年 | 選擇題數：0 | 申論題數：6

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所屬科目：研究所、轉學考(插大)◆工程數學

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申論題 (6)

1. Solve the following system of equations using the method of GaussJordan elimination.(25%) \[ x_1 + x_2 + 2x_3 + 6x_4 = 11 \]
\[ 2x_1 + 3x_2 + 6x_3 + 19x_4 = 36 \]
\[ 3x_2 + 4x_3 + 15x_4 = 28 \]
\[ x_1 - x_2 - x_3 - 6x_4 = -12 \]


a. Find the homogeneous solution yℎ
(10%)

b. Find the solution of the ODE(15%)


a. Find the homogeneous solution yℎ(10%)

b. Find the solution of the ODE(15%)

4. The following vectors form a basis for R3.Use these vectors in theGram-Schmidt process to construct an orthonormal basis for R3(1,1,1),(2,0,1),(2,4,5)(25%).