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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
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題組內容
II. The four eigenvalue of a 4x4 matrix A are 1, 1, 2, and 3. Please determine the correctness of the following descriptions.
10. The matrix A is a simple matrix.
其他申論題
6. The determinant of A is 6.
#450117
7. The trace of A is 7.
#450118
8. The rank(A-1)=3, where I is the 4x4 identity matrix.
#450119
9. The determinant of the adjoint matrix At is 6.
#450120
11. The row space of A is equal to the row space of B.
#450122
12. The column space of A is equal to the column space of B.
#450123
13. The null space of A is equal to the null space of B.
#450124
14. The rank(A) is equal to the rank(B).
#450125
15. The determinant of A is equal to the determinant of B.
#450126
16. If A and B are invertible 2x2 matrices, then
#450127
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