Question

线性代数求大神解答

Answer 1

简单计算一下，答案如图所示

Answer 2

写出增广矩阵为

1 1 1 1 1 1
3 2 1 1 -3 0
0 1 2 2 6 3
5 4 3 3 -1 2 r2-3r1,r4-5r1
~
1 1 1 1 1 1
0 -1 -2 -2 -6 -3
0 1 2 2 6 3
0 -1 -2 -2 -6 -3 r1+r2,r2+r3,r4+r3，交换r2r3
~
1 0 -1 -1 -5 -2
0 1 2 2 6 3
0 0 0 0 0 0
0 0 0 0 0
那么R(A,b)=R(A)=2 <5
于是有无穷多个解
基础解系为c1(1,-2,1,0,0)^T+ c2(1,-2,0,1,0)^T+c3(5,-6,0,0,1)^T+(-2,3,0,0,0)^T
c1c2c3为常数