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題組內容

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

19.If T， then Null(T)= span

其他申論題

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).

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).

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