若线性方程组x1+x2=a1,x2+x3=a2,x3+x4=a3,x4+x1=a4有解,则常数a1,a2,a3,a4应满足关系式?
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![若线性方程组x1+x2=a1,x2+x3=a2,x3+x4=a3,x4+x1=a4有解,则常数a1,a2,a3,a4应满足关系式?](/uploads/image/z/800347-67-7.jpg?t=%E8%8B%A5%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84x1%2Bx2%3Da1%2Cx2%2Bx3%3Da2%2Cx3%2Bx4%3Da3%2Cx4%2Bx1%3Da4%E6%9C%89%E8%A7%A3%2C%E5%88%99%E5%B8%B8%E6%95%B0a1%2Ca2%2Ca3%2Ca4%E5%BA%94%E6%BB%A1%E8%B6%B3%E5%85%B3%E7%B3%BB%E5%BC%8F%3F)
若线性方程组x1+x2=a1,x2+x3=a2,x3+x4=a3,x4+x1=a4有解,则常数a1,a2,a3,a4应满足关系式?
若线性方程组x1+x2=a1,x2+x3=a2,x3+x4=a3,x4+x1=a4有解,则常数a1,a2,a3,a4应满足关系式?
若线性方程组x1+x2=a1,x2+x3=a2,x3+x4=a3,x4+x1=a4有解,则常数a1,a2,a3,a4应满足关系式?
x1+x2 =a1
x2+x3 =a2
x3+x4=a3
x1 +x4=a4
增广矩阵(A,b)=
1 1 0 0 a1
0 1 1 0 a2
0 0 1 1 a3
1 0 0 1 a4
r4-r1得
1 1 0 0 a1
0 1 1 0 a2
0 0 1 1 a3
0 -1 0 1 a4-a1
r1+r4,r2+r4
1 0 0 1 a4
0 0 1 1 a2+a4-a1
0 0 1 1 a3
0 -1 0 1 a4-a1
r2r4
1 0 0 1 a4
0 -1 0 1 a4-a1
0 0 1 1 a3
0 0 1 1 a2+a4-a1
r4-r3
1 0 0 1 a4
0 -1 0 1 a4-a1
0 0 1 1 a3
0 0 0 0 a2+a4-a1-a3
因为线性方程有解
所以a2+a4-a1-a3=0
答案:a2+a4-a1-a3=0
55555555555555.......................
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