[試題] 98上 蕭浩明 工程數學上 期末考

[laba888 (喇叭)]

課程名稱︰工程數學上
課程性質︰系定必修
課程教師︰蕭浩明
開課學院：工學院
開課系所︰機械工程學系
考試日期（年月日）︰2010/01/11
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）

試題 :

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%)


--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 111.249.2.203
推 bookh       :感謝分享