求非齐次线性方程组的基础解系及其通解 X1-5X2+2X3-3X4=11 3X2+6X3-X4=1 2X1+4X2+2X
2个回答
增广矩阵 =
1 -5 2 -3 11
0 3 6 -1 1
2 4 2 1 -6
r3-2r1
1 -5 2 -3 11
0 3 6 -1 1
0 14 -2 7 -28
r3-5r2
1 -5 2 -3 11
0 3 6 -1 1
0 -1 -32 12 -33
r1-5r3,r2+3r3
1 0 162 -63 176
0 0 -90 35 -98
0 -1 -32 12 -33
r2*(-90)
1 0 162 -63 176
0 0 1 -7/18 49/45
0 -1 -32 12 -33
r1-162r2,r3+32r2
1 0 0 0 -2/5
0 0 1 -7/18 49/45
0 -1 0 -4/9 83/45
r3*(-1),r3r2
1 0 0 0 -2/5
0 1 0 4/9 -83/45
0 0 1 -7/18 49/45
基础解系为 (0,-8,7,18)'
通解为:(-2/5,-83/45,49/45,0)' + c(0,-8,7,18)',c为任意常数
