如题所述
没什么核心,就是化行最简形
解: 增广矩阵 =
1 3 5 -4 0 1
1 3 2 -2 1 -1
1 -2 1 -1 -1 3
1 -4 1 1 -1 3
1 2 1 -1 1 -1
ri-r1, i=2,3,4,5
1 3 5 -4 0 1
0 0 -3 2 1 -2
0 -5 -4 3 -1 2
0 -7 -4 5 -1 2
0 -1 -4 3 1 -2
r1+3r5,r3-5r5,r4-7r5,r5*(-1)
1 0 7 5 3 -5
0 0 -3 2 1 -2
0 0 16 -12 -6 12
0 0 24 -16 -8 16
0 1 4 -3 -1 2
r1-3r2,r3+6r2,r4+8r2,r5+r2 (这样可避免分数运算)
1 0 -2 -1 0 1
0 0 -3 2 1 -2
0 0 -2 0 0 0
0 0 0 0 0 0
0 1 1 -1 0 0
r3*(-1/2),r1+2r3,r2+3r3,r5-r3
1 0 0 -1 0 1
0 0 0 2 1 -2
0 0 1 0 0 0
0 0 0 0 0 0
0 1 0 -1 0 0
所以方程组的全部解为: (1,0,0,0,-2)^T+c(1,1,0,1,-2)^T.追问
解: 增广矩阵 =
1 3 5 -4 0 1
1 3 2 -2 1 -1
1 -2 1 -1 -1 3
1 -4 1 1 -1 3
1 2 1 -1 1 -1
ri-r1, i=2,3,4,5
1 3 5 -4 0 1
0 0 -3 2 1 -2
0 -5 -4 3 -1 2
0 -7 -4 5 -1 2
0 -1 -4 3 1 -2
r1+3r5,r3-5r5,r4-7r5,r5*(-1)
1 0 7 5 3 -5
0 0 -3 2 1 -2
0 0 16 -12 -6 12
0 0 24 -16 -8 16
0 1 4 -3 -1 2
r1-3r2,r3+6r2,r4+8r2,r5+r2 (这样可避免分数运算)
1 0 -2 -1 0 1
0 0 -3 2 1 -2
0 0 -2 0 0 0
0 0 0 0 0 0
0 1 1 -1 0 0
r3*(-1/2),r1+2r3,r2+3r3,r5-r3
1 0 0 -1 0 1
0 0 0 2 1 -2
0 0 1 0 0 0
0 0 0 0 0 0
0 1 0 -1 0 0
所以方程组的全部解为: (1,0,0,0,-2)^T+c(1,1,0,1,-2)^T.追问
怎么样就是行最简呢?是不是要先化成阶梯形的?可是我看到你的过程中没有额?
追答乖乖 还真没化完呢
1 0 0 -1 0 1
0 0 0 2 1 -2
0 0 1 0 0 0
0 0 0 0 0 0
0 1 0 -1 0 0
继续
r2*(1/2), r1+r2,r5+r2
1 0 0 0 1/2 0
0 0 0 1 1/2 -1
0 0 1 0 0 0
0 0 0 0 0 0
0 1 0 0 1/2 -1
交换行
1 0 0 0 1/2 0
0 1 0 0 1/2 -1
0 0 1 0 0 0
0 0 0 1 1/2 -1
0 0 0 0 0 0
所以方程组的全部解为: (0,-1,0,-1,0)^T+c(1,1,0,1,-2)^T.
你是老师么?谢谢老师,我解线性方程没方向,解到最后就乱套了,想让老师说下思路
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