线性方程组 x1+x3+x4-x5=1,x2-x3-x4=-1,2x2-x5=0,x1-x3+x4=0帮我解出来

Question

线性方程组 x1+x3+x4-x5=1,x2-x3-x4=-1,2x2-x5=0,x1-x3+x4=0帮我解出来

Answer 1

增广矩阵 =
1 0 1 1 -1 1
0 1 -1 -1 0 -1
0 2 0 0 -1 0
1 0 -1 1 0 0
r4-r1,r3-2r2
1 0 1 1 -1 1
0 1 -1 -1 0 -1
0 0 2 2 -1 2
0 0 -2 0 1 -1
r3*(-1/2),r1-r3,r2+r3,r4+2r3
1 0 0 0 -1/2 0
0 1 0 0 -1/2 0
0 0 1 1 -1/2 1
0 0 0 2 0 1
r4*(1/2),r3-r4
1 0 0 0 -1/2 0
0 1 0 0 -1/2 0
0 0 1 0 -1/2 1/2
0 0 0 1 0 1/2
方程组的解为:(0,0,1/2,1/2,0)'+c(1,1,1,0,1)