109年 - 109 國立中山大學_碩士班招生考試_資工系(乙組)：工程數學#105759

科目：中山◆資工◆工程數學 | 年份：109年 | 選擇題數：0 | 申論題數：30

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所屬科目：中山◆資工◆工程數學

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申論題 (30)

1.All circulant matrices are made diagonal by the Discrete Fourier Transform (DFT), regardless of the generating vector x.

2..DFT matrix is not a kind of symmetric matrix.

3. DFT matrix is an unitary matrix.

4.The DFT is a linear transform.

5. The orthogonality is not the property of the DFT matrix.

6. The determinant of A is 6.

7. The trace of A is 7.

8. The rank(A-1)=3, where I is the 4x4 identity matrix.

9. The determinant of the adjoint matrix At is 6.

10. The matrix A is a simple matrix.

11. The row space of A is equal to the row space of B.

12. The column space of A is equal to the column space of B.

13. The null space of A is equal to the null space of B.

14. The rank(A) is equal to the rank(B).

15. The determinant of A is equal to the determinant of B.

16. If A and B are invertible 2x2 matrices, then

17. If A is a 3x3 matrix such that the system Ax = 0 has only the trivial solution, then the equation Ax = b is consistent for every b in R³.

18. If P and D are nxn matrices, then det = det(D).

19.If T， then Null(T)= span

20. If A and B are any 2x2 matrices, then AB = BA.

21. The matrix is not invertible.

22. The matrix of the linear transformation T which reflects points about the x-axis and then about the y-axis is the same as the matrix of the linear transformation S which rotates points about the origin by 180 degrees counterclockwise.

23. If V is a set that contains the 0-vector, and such that whenever u and y are in V, then u t v is in V, then Vis a vector space.

24. If A and B are square matrices, then

25. If A and B are square matrices, then det(A + B) = det(A) +det(B).

26. For every t∈ (-20,55), the following series can be converged.

27. For every integer n≥ I, we have 10

28. For every integer n ≥ 1, we have

29. For every t∈ (-2,3), we have

30. We have