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題組內容

IV. Please read the following True/False questions and determine the correctness of cach description.

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

其他申論題

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.

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.

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