Question

线性代数习题 求助第4题还有第6题。。求过程

Answer 1

4（1）A =
1 2 3 4
1 -2 4 5
1 10 1 2
=
1 2 3 4
0 -4 1 1
0 8 -2 -2
=
1 2 3 4
0 -4 1 1
0 0 0 0
R(A) = 2

（2）A =
0 1 1 -1 2
0 2 2 2 0
0 -1 -1 1 1
1 1 0 0 -1
=
1 1 0 0 -1
0 2 2 2 0
0 -1 -1 1 1
0 1 1 -1 2
=
1 1 0 0 -1
0 1 1 -1 2
0 -1 -1 1 1
0 2 2 2 0
=
1 1 0 0 -1
0 1 1 -1 2
0 0 0 0 3
0 0 0 4 -4
=
1 1 0 0 -1
0 1 1 -1 2
0 0 0 4 -4
0 0 0 0 3
R(A) = 4

6. A =
2 3 11 5 2
1 1 5 2 1
2 1 3 2 -3
1 1 3 4 -3
=
1 0 0 0 -2
0 1 0 0 0
0 0 1 0 1
0 0 0 1 -1
所以
x1 = -2,
x2 = 0,
x3 = 1,
x4 = -1