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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
IV. Please read the following True/False questions and determine the correctness of cach description.
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 R
3
.
其他申論題
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
18. If P and D are nxn matrices, then det = det(D).
#450129
19.If T， then Null(T)= span
#450130
20. If A and B are any 2x2 matrices, then AB = BA.
#450131
21. The matrix is not invertible.
#450132
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.
#450133
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.
#450134
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