課程名稱︰管理數學
課程性質︰必修
課程教師︰謝承熹
開課學院：管理學院
開課系所︰財金系
考試日期（年月日）︰2016/11/08
考試時限（分鐘）：120分鐘
試題 :
I (72 points) Answer each of the following as True or False. Justify your answer
, otherwise you cannot get any point. Moreover, please give your answer
in order. Thanks!
For Q1~Q10, let A and B be nxn matrices.
1. If A and B are scalar matrices, then AB is a scalar matrix.
2. If A and B are symmetric, then AB is symmetric.
3. If A and B are upper triangular, then AB is upper triangular.
4. If A and B are skew symmetric, then A+B is skew symmetric.
5. If A and B are in reduced row echelon form, then A+B is in reduced row
echelon form.
6. If A and B are nonsingular, then A+B is nonsingular.
7. If A and B are singular, then A+B is singular.
8. If A and B are idempotent, then A+B is idempotent.
9. If Trace(A) = Trace(B) = 1, then Trace(A+B) = 1.
10.If det(A) = det(B) = 1, then det(A+B) = 1.
11.If c and d are solutions of Ax=0, then c+d is a solution of Ax=0.
12.If c and d are solutions of Ax=b, then c+d is a solution of Ax=b.
II (14 points) Let A = [ai,j], where ai,j = xi^(j-1) for i = 1,2,3,4 and
j = 1,2,3,4. Find det(A).
III(10 points)(a) Let L:R2