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中原大學九十三學年度碩士班入學招生考試
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| 93年3月27日 11:00~12:30 資訊工程學系 | 誠實是我們珍視的美德， 我們喜愛「拒絕作弊，堅守正直」的你！ |
| 科目：計算機數學 |
| 1. | Determine the determinant and the inverse of the following matrix. (13%) | |
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| 2. | Transform 
to an orthonormal basis 
under the Euclidean inner product using the Gram-Schmidt process (beginning
from  ).
=(1,2,
0),  =(1,1,
1), =(0,2,
1). (15%) |
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| 3. | Determine the eigenvalues and eigenspaces for the following matrix. (10%) | |
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| 4. | Determine the standard matrix of the linear transformation
that orthogonally projects any 
vector onto the line L? 需寫計算過程(12%) |
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| 5. | Please prove "Finite Induction Principle (Principle of Mathematical Induction)" by "Well-Ordering Principle" (10%) | |
| 6. | Let |A|=5. (a) How many functions f: A*A->A are there? (b) How many closed binary operations are there on A? (c) How many of these closed binary operations are commutative? (15 %) | |
| 7. | Let M be the finite state machine given in the state diagram as shown below, please draw the state table and minimize machine M. (15 %) | |
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| 8. | For each of the following relations, determine whether the relation is reflexive, symmetric, antisymmetric, or transitive. (10 %) | |
(1)  where
a R b if a|b (read "a divides b")(2) R is relation on Z where x R y if x +y is odd |
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