沧月哀荒1
习题四（A类）
1.用消元法解下列方程组.
x1+4x2 2x3+3x4=6, 2x+2x+4x=2, 124
3x1+2x2+2x3 3x4=1, x+2x2+3x3 3x4=8;(1) 1
【解】(1)
(2)
x1+2x2+2x3=2,
2x1+5x2+2x3=4, x+2x+4x=6; 123
6
r4 r1
1 r2 r1 →r3 3r2 1 8
1 2
(A b)=
3 1
4 2320422 323 3
6 1
11
r2 2 2 →
31
8 1
4 23
10222 323 3
14 236 0 32 1 5
( 1) r2 r3
→ 0 12 9 2 0 25 62 14 236 1 01 292 0
r+3r32 → r4+2r2
0 32 1 5 0 0 25 62 0 1 0 0 0
得
4 231 290 4260112
4 236 1
01 292 r+4r43 → 001126
0 4261 0
4
100
6 2 r4 r3 →1 6
236 292 ,1126
07425
x1+4x2 2x3+3x4=6 x 2x+9x=2 234
x3+12x4=6 74x4=25
所以
