线性方程组题目x1+x2-2x3+3x4=02x1+x2-6x3+4x4=-13x1+2x2+k1x3+7x4=-1x1

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线性方程组题目
x1+x2-2x3+3x4=0
2x1+x2-6x3+4x4=-1
3x1+2x2+k1x3+7x4=-1
x1-x2-6x3-x4=k2
K1,K2各为何值时,方程组有唯一解?有无穷多解?有无穷多解时求全部解.

增广矩阵 =
1 1 -2 3 0
2 1 -6 4 -1
3 2 k1 7 -1
1 -1 -6 -1 k2
r2-r1-r2,r2-2r1,r4-r1
1 1 -2 3 0
0 -1 -2 -2 -1
0 0 k1+8 0 0
0 -2 -4 -4 k2
r1+r2,r4-2r2,r2*(-1)
1 0 -4 1 -1
0 1 2 2 1
0 0 k1+8 0 0
0 0 0 0 k2+2
当k2≠-2时,方程组无解 (这叫做非零的尾巴,有它就无解)
当k2=-2时,方程组有无穷多解.
此时再分两种情况:
(1)当k1≠-8时,所有解为 (-1,1,0,0)'+c(1,2,0,-1)'.
(2)当k1=-8时,所有解为 (-1,1,0,0)'+c1(4,-2,1,0)+c2(1,2,0,-1)'.

求非齐次线性方程组：2x1-x2+4x3-3x4=-4;x1+x3-x4=-3;3x1+x2+x3=1;7x1+7x3- 解线性方程组求齐次线性方程组X1+X2+X3+X4=0,2X1+3X2+4X3+5X4=0,4X1+5X2+6X3+7 求线性方程组 x2-x3-x4=0 x1+x2-x3+3x4=1 x1-x2+x3+5x4=-1 x1+2x2-2x3+ 求齐次线性方程组x1+2x2+x3+x4+x5=1 2x1+4x2+3x3+x4+x5=2 -x1-2x2+x3+3x4 线性方程组线性方程组1x1+x2 -2x4=-64x1-x2-x3-x4=13x1-x2-x3 =3方程组2X1+MX 解线性方程组求齐次线性方程组X1+X2+X3+X4=0,2X1+3X2-X3-2X4=0,5X1+6X2+2X3+X4 求非齐次线性方程组的通解：2x1+x2-x3-x4=1;2x1+x2+x3-x4=1;4x1+2x2+x3-2x4=2 .解线性方程组｜X1+X2+X3+X4=5 ｜X1+2X2-X3+4X4=-2 ｜2X1-3X2-X3-5X4=-2 ｜设齐次线性方程组:x1+x2+x3+x4=0,x2-x3+2x4=0,2x1+3x2+(a+2)x3+4x4=0,3x1 求齐次线性方程组{X1+X2+3X3+2X4=0 2X1+3X2+X3-X4=0 5X1+6X2+10X3+5X4=0} 奇次线性方程组x1-2x2+3x3-4x4=0 x2-x3+x4=0 x1+3x2-kx4=0 -7x2+kx3+x4= 用列主元Gauss消元法解线性方程组{-x2-x3+x4=0,x1-x2+x3-3x4=1,2x1-2x2-4x3+6x