感激不尽求线性方程组基础解系x1+x2+3x4-x5=0x1-x2+2x3-x4=04x1-2x2+6x3+3x4-4x

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/28 08:25:27

感激不尽
求线性方程组基础解系
x1+x2+3x4-x5=0
x1-x2+2x3-x4=0
4x1-2x2+6x3+3x4-4x5=0
2x1+4x2-2x3+4x4-7x5=0

系数矩阵 A=
[1 1 0 3 -1]
[1 -1 2 -1 0]
[4 -2 6 3 -4]
[2 4 -2 4 -7]
行初等变换为
[1 1 0 3 -1]
[0 -2 2 -4 1]
[0 -6 6 -9 0]
[0 2 -2 -2 -5]
行初等变换为
[1 1 0 3 -1]
[0 2 -2 4 -1]
[0 0 0 3 -3]
[0 0 0 -6 -4]
行初等变换为
[1 1 0 3 -1]
[0 2 -2 4 -1]
[0 0 0 1 -1]
[0 0 0 0 -10]
行初等变换为
[1 1 0 3 -1]
[0 2 -2 4 -1]
[0 0 0 1 -1]
[0 0 0 0 1]
方程组同解变形为
x1+x2+3x4-x5=0
2x2+4x4-x5=2x3
x4-x5=0
x5=0
取x3=1,得基础解系 (-1,1,1,0,0)^T.

感激不尽求线性方程组基础解系x1+x2+3x4-x5=0x1-x2+2x3-x4=04x1-2x2+6x3+3x4-4x 齐次线性方程组{X1+X2+3X3+X4=0;2X1-X2+X3-3X4=0;X1+X3-X4=0}的基础解系求齐次线性方程组x1+2x2+x3+x4+x5=1 2x1+4x2+3x3+x4+x5=2 -x1-2x2+x3+3x4 求线性方程组{X1+X2+2X3-3X4=0; X1+2X2-X3+2X4=0; 2X1+3X2+X3-X4=0}的基础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 求线性方程组 x2-x3-x4=0 x1+x2-x3+3x4=1 x1-x2+x3+5x4=-1 x1+2x2-2x3+ 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 求线性方程组一般解,2X1+X2-2X3+3X4=03X1+2X2-X3+2X4=0X1+X2+X3-X4=0 求线性方程组的全部解x1+x2-3x4-x5=2x1-x2+2x3-x4=14x1-2x2+6x3+3x4-4x5=82 简单线代题///X1+X2+X3+X4+X5=13X1+2X2+X3+X4+3X5=0 X2+2X3+2X4+6X5=3 X1 - X3 - X4 -5X5=0 X1+2X2+3X3+3X4+7X5=0 X1+X2+X3+X4+X5=0 X2 解方程组X2+X3+X4=1 X1+X2+X3=5 X3+X4+X5=-5 X4+X5+X1=-3 X5+X1+X2=2