1. 解方程組
62x + 93y - 155z = 186
148x - 74y + 259z = 333
252x + 82y - z = 645
2. 解方程組
133a - 95b + 76c + 152d = 171
204a + 102b - 68c - 136d = 374
319a + 174b + 232c - 203d = 667
85a - 241b - 94c + 341d = -32
【註：如無法求唯一解，請找出方程組中哪一/些式子是由其餘式子經過怎樣的運算得來。如：a+b=0 --(1)，c-b=1 --(2)，a+c=1 --(3)，(3)是由(1)+(2)得來的。】
解三、四元一次方程組兩題
2011-12-13 4:59 am
回答 (3)
2011-12-18 2:24 am
2011-12-18 7:36 am
1.
62x + 93y - 155z = 186 i
148x - 74y + 259z = 333 ii
252x + 82y - z = 645 iii
由iii
252x+82y-645=z iv
代iv入i和ii
62x+93y-155(252x+82y-645)=186 <<<i
62x+93y-39060x-12710y+99975=186
-38998x-12617y=-99789
38998x+12617y=99789 v
148x - 74y + 259(252x+82y-645 )= 333 <<<ii
148x-74y+65268x+21238y-167055=333
65416x+21164y=167388
16129x+5291y=41847
(16129x-41847)/-5291=y vi
代vi入v
38998x+12617(41847-16129x)/5291=333
38998x+99789-31/13(41847)x=333
-60791x=-99456
x=1.64
代x=1.64入vi
(16129*1.64-41847)/-5291=y
y=2.91
代 x=1.64 and y=2.91 入iii
252*1.64+82*2.91-z=645
z=6.9
所以
(x,y,z)=(1.64,2.91,6.9
2.
133a - 95b + 76c + 152d = 171 i
204a + 102b - 68c - 136d = 374 ii
319a + 174b + 232c - 203d = 667 iii
85a - 241b - 94c + 341d = -32 iv
由iv
85a-241b+341d-32=94c
c=(85a-241b+341d-32)/94 v
代v入i,ii和iii
133a-95b+3230a/47-9158b47+12958d/47-1216/47+152d=171 <<<i
8481a/47-4693b/47+20102d/47-9253/47=0
9481a-4693b+20102d-9253=0
(9481a-4693b-9253)/20102=d vi
204a+102b-2890a/47-8194b/47-11594/47+136d-1088d/47=374 <<<ii
6698a/47-3400b/47+5304d/47-29172=0
6698a-340b+534d-29172=0
3349a-1700b+2652d-14586=0 vii
319a+174b+9860a/47-55912b/47+39556d/47+39556d/47-3712/47-203d=667<<<iii
24853a/47-47734b/47+30015d/47-35061=0
24853a-47734b+3015d-3561=0 viii
(9481a-4693b-9253)/20102=d vi
3349a-1700b+2652d-14586=0 vii
24853a-47734b+3015d-3561=0viii
代vi入vii和viii
3349a-1760b-12571806a/10051+6222918b/10051-1226978/10051-14586=0<<<vii
2098.19849a+22379.13422b-14708.07522=0 ix
26275.00851a-48437.87996b-4948.81191=0 <<<viii
(26275.00851a-4948.81191)/48437.87996=b x
代x入ix
2098.19849a+22379.13422(26275.00851a-4948.81191)/48437.87996-14708.07522=0
14237.70465a=16992.4615
a=1.19
代a=1.19入x
26275.00851(1.19-4948.41191)/48437.87996=b
b=0.543
代a=1.19,b=0.543入 vi
(9481*1.19 -4693*0.543-9253)/20102=d
d=-0.258
代 a=1.19,b =0.543,d=-0.258 入v
c=(85*1.19 -241*0.543 +341*-0.258 -32)/94
c=-1.59
所以
(a,b,c,d)=(1.19,0.543,-1.59,-0.258)
62x + 93y - 155z = 186 i
148x - 74y + 259z = 333 ii
252x + 82y - z = 645 iii
由iii
252x+82y-645=z iv
代iv入i和ii
62x+93y-155(252x+82y-645)=186 <<<i
62x+93y-39060x-12710y+99975=186
-38998x-12617y=-99789
38998x+12617y=99789 v
148x - 74y + 259(252x+82y-645 )= 333 <<<ii
148x-74y+65268x+21238y-167055=333
65416x+21164y=167388
16129x+5291y=41847
(16129x-41847)/-5291=y vi
代vi入v
38998x+12617(41847-16129x)/5291=333
38998x+99789-31/13(41847)x=333
-60791x=-99456
x=1.64
代x=1.64入vi
(16129*1.64-41847)/-5291=y
y=2.91
代 x=1.64 and y=2.91 入iii
252*1.64+82*2.91-z=645
z=6.9
所以
(x,y,z)=(1.64,2.91,6.9
2.
133a - 95b + 76c + 152d = 171 i
204a + 102b - 68c - 136d = 374 ii
319a + 174b + 232c - 203d = 667 iii
85a - 241b - 94c + 341d = -32 iv
由iv
85a-241b+341d-32=94c
c=(85a-241b+341d-32)/94 v
代v入i,ii和iii
133a-95b+3230a/47-9158b47+12958d/47-1216/47+152d=171 <<<i
8481a/47-4693b/47+20102d/47-9253/47=0
9481a-4693b+20102d-9253=0
(9481a-4693b-9253)/20102=d vi
204a+102b-2890a/47-8194b/47-11594/47+136d-1088d/47=374 <<<ii
6698a/47-3400b/47+5304d/47-29172=0
6698a-340b+534d-29172=0
3349a-1700b+2652d-14586=0 vii
319a+174b+9860a/47-55912b/47+39556d/47+39556d/47-3712/47-203d=667<<<iii
24853a/47-47734b/47+30015d/47-35061=0
24853a-47734b+3015d-3561=0 viii
(9481a-4693b-9253)/20102=d vi
3349a-1700b+2652d-14586=0 vii
24853a-47734b+3015d-3561=0viii
代vi入vii和viii
3349a-1760b-12571806a/10051+6222918b/10051-1226978/10051-14586=0<<<vii
2098.19849a+22379.13422b-14708.07522=0 ix
26275.00851a-48437.87996b-4948.81191=0 <<<viii
(26275.00851a-4948.81191)/48437.87996=b x
代x入ix
2098.19849a+22379.13422(26275.00851a-4948.81191)/48437.87996-14708.07522=0
14237.70465a=16992.4615
a=1.19
代a=1.19入x
26275.00851(1.19-4948.41191)/48437.87996=b
b=0.543
代a=1.19,b=0.543入 vi
(9481*1.19 -4693*0.543-9253)/20102=d
d=-0.258
代 a=1.19,b =0.543,d=-0.258 入v
c=(85*1.19 -241*0.543 +341*-0.258 -32)/94
c=-1.59
所以
(a,b,c,d)=(1.19,0.543,-1.59,-0.258)
2011-12-13 5:10 am
use matrix la
收錄日期: 2021-04-23 23:25:24
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https://hk.answers.yahoo.com/question/index?qid=20111212000051KK00684