刘老师好,我有几道线性代数题求解!

1.
解: A-->
r2-2r3, r1-2r2
0 0 15 -9
1 0 -8 6
0 1 3 -1
r1*(1/15), r2+8r1,r3-3r1
0 0 1 -3/5
1 0 0 6/5
0 1 0 4/5
交换行
1 0 0 6/5
0 1 0 4/5
0 0 1 -3/5
2.
r1-r3,r2-2r3
0 1 1 1
0 1 1 1
2 0 1 2

r1-r2, r3*(1/2)
0 0 0 0
0 1 1 1
1 0 1/2 1
交换行
1 0 1/2 1
0 1 1 1
0 0 0 0
3.
(A,E)=
1 0 2 1 1 0 0 0
1 2 1 2 0 1 0 0
0 0 0 1 0 0 1 0
0 0 1 0 0 0 0 1
r1-r3,r2-2r3, r1-2r4,r2-r4
1 0 0 0 1 0 -1 -2
1 2 0 0 0 1 -2 -1
0 0 0 1 0 0 1 0
0 0 1 0 0 0 0 1
r2-r1
1 0 0 0 1 0 -1 -2
0 2 0 0 -1 1 -1 1
0 0 0 1 0 0 1 0
0 0 1 0 0 0 0 1
r2*(1/2),r3r4
1 0 0 0 1 0 -1 -2
0 1 0 0 -1/2 1/2 -1/2 1/2
0 0 1 0 0 0 0 1
0 0 0 1 0 0 1 0
所以 A^-1=
1 0 -1 -2
-1/2 1/2 -1/2 1/2
0 0 0 1
0 0 1 0

PS. 提问时尽量把题目分开提问, 每题悬赏20答的人就不少了