課程名稱︰工程數學一
課程性質︰土木系大二必修
課程教師︰張書瑋
開課學院：工學院
開課系所︰土木系
考試日期（年月日）︰2015.11.2
考試時限（分鐘）：50 分鐘
試題 :
Engineering Mathematics(I) Quiz 2
1. Find the inverse by Determinants. (10%)
┌ 0 1/2 0 ┐
│ │
│ 0 0 1/4│
│ │
└1/8 0 0 ┘
2. Find the inverse by Gauss-Jordan Method.(10%)
┌ 1 0 0 ┐
│ │
│-2 1 0 │
│ │
└ 5 -4 1 ┘
3. Find the eigenvalues and the corresponding eigenvectors.(25%)
┌ 3 5 3 ┐
│ │
│ 0 4 6 │
│ │
└ 0 0 1 ┘
4. Given A in a deformation y = Ax, find the principle directions.(15%)
┌ 1 2√2 ┐
A = │ │
└2√2 -1 ┘
5. Classify the following matrices.(symmetric, skew-symmetric, orthogonal)(15%)
┌ 3 0 0 ┐ ┌ 0 -1 -1/2 ┐ ┌ 0 0 -1 ┐
│ │ │ │ │ │
A1 = │ 0 -1 √3│,A2 = │ 1 0 1 │,A3 = │ 0 -1 0 │
│ │ │ │ │ │
└ 0 √3 1 ┘ └1/2 -1 0 ┘ └ 1 0 0 ┘
6. Find an eigenbasis (a basis of eigenvectors) and diagonalize. Show the
details.(25%)
┌ -1 -1 0 ┐
│ │
│ -1 -1 0 │
│ │
└ 0 0 2 ┘