Question

求教一道线代题

请问第26题答案中划蓝线的那几个解是怎么得出来的？

Answer 1

即写出增广矩阵
1 1 -1 1
2 a+2 -b-2 3
0 -3a a+2b -3 r2-2r1
~
1 1 -1 1
0 a -b 1
0 -3a a+2b -3 r3+3r2
~
1 1 -1 1
0 a -b 1
0 0 a-b 0
显然系数行列式=a(a-b)
不等于零即a不等于0，且a不等于b
~
1 1 -1 1
0 a -b 1
0 0 1 0 r1+r3，r2+br3
~
1 1 0 1
0 a 0 1
0 0 1 0 r2/a，r1-r2
~
1 0 0 1-1/a
0 1 0 1/a
0 0 1 0
于是x1=1-1/a，x2=1/a，x3=0