Question

讨论2X1+X2-X3+X4=1 3X1-2X2+2X3-3X4=2 5X1+X2-X3+2X4=-1 2X1-X2+X3-3X4=4的解的情况

Answer 1

增广矩阵 A =
[2 1 -1 1 1]
[3 -2 2 -3 2]
[5 1 -1 2 -1]
[2 -1 1 -3 4]
线性变换为
[2 1 -1 1 1]
[6 -4 4 -6 4]
[10 2 -2 4 -2]
[2 -1 1 -3 4]
线性变换为
[2 1 -1 1 1]
[0 -7 7 -9 1]
[0 -3 3 -1 -7]
[0 -2 2 -4 3]
线性变换为
[2 1 -1 1 1]
[0 1 -1 2 -3/2]
[0 0 0 5 -19/2]
[0 0 0 5 -23/2]
线性变换为
[2 1 -1 1 1]
[0 1 -1 2 -3/2]
[0 0 0 5 -19/2]
[0 0 0 0 -2]
增广矩阵的秩是4,系数矩阵的秩是3,方程组无解.