51D3?0001?0065100651100010006510006556510按第三列展开1000510006510065?5100651000650006
6?61500?19?6?114?703 651D4?00065100065105100016510006506??395 5按第四列展开1?000510065100065?5100651006510006
??5?61051D5?000?6510006510150766500651;10001x2??1145665;1按最后一列展开510070366565100651?395665212665000?D??1?211?212
x1?x3?;x4?;x4?．
9.问?,?取何值时,齐次线性方程组??x1?x2?x3?0??x1??x2?x3?0有非零解？ ??x1?2?x2?x3?0?111?????， 1解 D3?11?2?16
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??2x1?(3??)x2?x3?0 ??x1?x2?(1??)x3?010.问?取何值时,齐次线性方程组有非零解？ 解
1??D?213?23??1411???1??21?3??1??0411??
?(1??)?(??3)?4(1??)?2(1??)(?3??) ?(1??)?2(1??)???3
32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.
17