Question

求线性代数答案6

Answer 1

1.
解: |A^-1|=2, |A|=1/2.
由 AA* = |A|E.
(A*)^-1 = |A|A = (1/2)A.

(A^-1,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 =
5/2 -1 -1/2
-1 1 0
-1/2 0 1/2

(A*)^-1 = (1/2)A
5/4 -1/2 -1/4
-1/2 1/2 0
-1/4 0 1/4

2.
(a1,a2,a3,a4,a5)=
1 1 1 4 -3
1 -1 3 -2 -1
2 1 3 5 -5
3 1 5 6 -7
用初等行变换化成行简化梯矩阵
1 0 2 1 -2
0 1 -1 3 -1
0 0 0 0 0
0 0 0 0 0
(1) a1,a2 是一个极大无关组
(2) a3=2a1-a2, a4=a1+3a2, a5=-2a1-a2
(3) 向量组的秩为2.

满意请采纳^_^.
PS. 以后最好一个题目提个问题, 一次答几个太累人了哈