张家港学数学哪里好

沙洲西路名思不错的

2. 解:
r3-2r1-2r2, r1-4r2
0 -7 2 -4
1 2 0 2
0 -1 -2 -12
0 1 1 7
r1<->r2
1 2 0 2
0 -7 2 -4
0 -1 -2 -12
0 1 1 7
r2-7r3,r4+r3
1 2 0 2
0 0 16 80
0 -1 -2 -12
0 0 -1 -5
r2+16r4
1 2 0 2
0 0 0 0
0 -1 -2 -12
0 0 -1 -5
行列式 = 0
3. 因为 (AA^T)^T = (A^T)^TA^T = AA^T, 所以 AA^T是对称矩阵.
因为 (A+A^T)^T = A^T+(A^T)^T = A^T+A = A+A^T, 所以 A+A^T 是对称矩阵.
4. (A,E) =
1 1 1 1 0 0
1 2 1 0 1 0
1 1 3 0 0 1
r2-r1,r3-r1
1 1 1 1 0 0
0 1 0 -1 1 0
0 0 2 -1 0 1
r3*(1/2)
1 1 1 1 0 0
0 1 0 -1 1 0
0 0 1 -1/2 0 1/2
r1-r2-r3
1 0 0 5/2 -1 -1/2
0 1 0 -1 1 0
0 0 1 -1/2 0 1/2
所以 A^-1 =
5/2 -1 -1/2
-1 1 0
-1/2 0 1/2
5.解: (a1^T,a2^T,a3^T,a4^T)
1 -2 2 3
0 3 1 2
-1 1 -1 -4
r3+r1
1 -2 2 3
0 3 1 2
0 -1 1 -1
r2+3r3
1 -2 2 3
0 0 4 -1
0 -1 1 -1
r2<->r3
1 -2 2 3
0 -1 1 -1
0 0 4 -1
所以向量组的秩为 3.