作者laba888 (喇叭)
看板NTU-Exam
标题[试题] 98上 萧浩明 工程数学上 期末考
时间Sun Dec 26 00:54:29 2010
课程名称︰工程数学上
课程性质︰系定必修
课程教师︰萧浩明
开课学院：工学院
开课系所︰机械工程学系
考试日期（年月日）︰2010/01/11
考试时限（分钟）：120
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
1. Use Gaussian-Jordan elimination to slove X (15%)
2X1 - 4X2 + X3 = 0
{ X1 + X2 + 4X3 = 5
3X1 + X2 - 3X3 = -1
2. Determine the eigenvalues and eigenvectors of (10%)
┌ ┐
│cosθ -sinθ│
A = │sinθ cosθ│
└ ┘
3. ┌ ┐
│1 0 2│
A = │2 1 1│
│1 1 1│
└ ┘
-1 T
Find A using (a) [A_ij] /|A| (b) elementary row operations (15%)
4. ┌ ┐
│1 1 -2│ 4 3 2
A = │-1 2 1│ evaluate 2A - 4A - 2A - 7A + 3I = ? (10%)
│0 1 -1│
└ ┘
-1
5. Transform the following matrix A to a diagonal matrix D using D = P AP
┌ ┐
│7 -2 1│
A = │-2 10 -2│ (15%)
│1 -2 7│
└ ┘
6. ┌ ┐ (15%)
│1 3│
A = │2 2│ (a) Determine its eigenvalues λ1 and λ2
└ ┘
* * -1
(b) Find the eigenvalues λ1 and λ2 of A
* *
(c) Find the relationship betweenλ1 and λ1 ,λ2 and λ2
7. Use the method of Frobenius to find the general solution near x=0 of
2 2
x y"+ xy'+ (x -1)y = 0 (20%)
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