沧月哀荒1
187 x= , 1
74
x=211, 274
x=144, 374 25 x4=.
74
(2)
x1+2x2+2x3=2
2x1+5x2+2x3=4 x+2x+4x=6 123
解② ①×2得
③ ①得得同解方程组
①②③
x2 2x3=02x3=4
x1+2x2+2x3=2
x2 2x3=0 2x=4 3
由⑥得x3=2,
由⑤得x2=2x3=4,由④得x1=2 2x3 2x2= 10,得(x1,x2,x3)T=( 10,4,2)T.2.求下列齐次线性方程组的基础解系.
④⑤⑥
(1)
x1+3x2+2x3=0,
x1+5x2+ x3=0, 3x+5x+8x=0; 123
x1+ x2+2x3+2x4+7x5=0,
2x1+3x2+4x3+5x4 =0, 3x+5x+6x+8x =0; 1234
(3)
【解】(1)
x1 x2+5x3 x4=0, x+ x 2x+3x=0, 1234
3x1 x2+8x3+ x4=0, x+3x2 9x3+7x4=0;(2) 1
x1+2x2 2x3+2x4 x5=0,
x1+2x2 x3+3x4 2x5=0, 2x+4x 7x+ x+ x=0. 12345
(4)
x1+3x2+2x3=0,
x1+5x2+x3=0, 3x+5x+8x=0. 123
132 132 132
r2 r1r3+2r2 02 1 02 1 A= 151 →→
r3 3r1 358 0 42 000
得同解方程组
