请大家确认几道题的答案

peterzhang1986UID：2519554

49.   The linear equation system

a 11 x 1 + a 12 x 2 + a 13 x 3 = b 1
a 21 x 1 + a 22 x 2 + a 23 x 3 = b 2
a 31 x 1 + a 32 x 2 + a 33 x 3 = b 3
a 41 x 1 + a 42 x 2 + a 43 x 3 = b 4

has exactly one solution. Let M be the augmented matrix of the linear
equation system, then which of the following statement may be false?
A. the rank of M is 3
B. there exists a line which is the combination of other three.
C. the determination of M is zero.
D. the fourth column is the combination of the first three columns.
E. M can become the unity matrix after elementary row matrix
transformation.

48. A ∪ B ∪ C  =68,   A  =47,   B  =25,   C  =15,   A ∩ B ∩ C  =7, how many
elements are exactly in two of {A,B,C}?

44. Consider the maps g which maps {1,2,3,4,5} onto {11,12,13,14} and
g(1) ≠ g(2), how many such g are there?

38. T(u)=u,  T(v)=2v,  T(w)=3w,  T  is  the  linear  transformation  of  R3,
which of the following is right:
Ⅰ. det(T)=6
Ⅱ. u, v, w are the bases of R3

Ⅲ.   xE − T  =(x-1)(x-2)(x-3)


33.   T is orthogonal, which of the following is right?
Ⅰ. Tu·Tv = u·v
Ⅱ. If v  ⊥   (  sqrt(2)/2 ,  sqrt(2)2 , 0), Tv·v=0
Ⅲ. T^2= I

dvorakUID：3398270

49.E
44. We know both 1-1, 1-2, 1-3, 1-4 mapping are possible, the image has 2^4=16 components. so the permutation or combination of this mapping may be 16P4