1 D4?12115?142
13?1?2202?3?1?2?D1x1??1,DD2x2??2,DD3x3??3,DD4x4???1
D56000156005600按最后一行1560?5D??6D?? (2)D?015605D??展开015000156001600015?5(5D???6D???)?6D???19D???30D??? ?65D????114D?????65?19?114?5?665
?的余子式(D?为行列式D中a11的余子式,D??为D?中a11,D???,D????类推)
160000560060005600按第一列D1?01560 D??1560展开00156015610015?D??64?19D????30?????64?1507 5100010600D2?0056016005000按第二列05601600 ??01560560展开001560015015601015560?156?5?63??65?1080??1145 015 16
561001500015005600按第三列01601500D3?01060 ?00560160展开000560015005600115160560?056?6150?19?6?114?703 015016560101560015605600按第四列01501560D4?01500 ??00160150展开001060005001600015560??5?6156??395
01556001156001560按最后一列0156D5?01560?D??1?211?212
展开001500150000100011?x1?15071145703?395212． ;x2??;x3?;x4?;x4?665665665665665??x1?x2?x3?0?11.问?,?取何值时,齐次线性方程组?x1??x2?x3?0有非零解？
?x?2?x?x?023?1?解 D3?11
1?1?????， 2?117
1齐次线性方程组有非零解，则D3?0 即 ?????0 得 ??0或??1
不难验证，当??0或??1时,该齐次线性方程组确有非零解.
?(1??)x1?2x2?4x3?0?12.问?取何值时,齐次线性方程组?2x1?(3??)x2?x3?0
?x?x?(1??)x?023?1有非零解？ 解
1??D?21?241??3??1?211??1?3??41??1 01???(1??)3?(??3)?4(1??)?2(1??)(?3??) ?(1??)3?2(1??)2???3
齐次线性方程组有非零解，则D?0 得 ??0,??2或??3
不难验证，当??0,??2或??3时，该齐次线性方程组确有非零解.
18