高等代数(北大版第三版)习题答案I.doc

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1、此资料由网络收集而来，如有侵权请告知上传者立即删除。资料共分享，我们负责传递知识。高等代数(北大版第三版)习题答案I篇一：高等代数(北大版)第3章习题参考第三章线性方程组1．用消元法解下列线性方程组：?x1?x?1?1)?x1?x?1??x1?3x2?5x3?4x4?1?3x2?2x3?2x4??2x2?x3?x4?x5?4x2?x3?x4?x5?2x2?x3?x4?x5?x1?2x2?3x4?2x5?1x5??1??x1?x2?3x3?x4?3x5?2?32)?2x?3x?4x?5x?2x?72345?1?3?9x?9x?6x?16x?2x?252345?1??1

2、x3?x7?0?3x1?4x2?5?x1?2x2?3x3?4x4?44??x3?x2?0?x2?x3?x4??3?2x1?3x2?3437此资料由网络收集而来，如有侵权请告知上传者立即删除。资料共分享，我们负责传递知识。3)?4)?4x?11x?13x?16x?0x?3x??x?123424?1?1??7x?3x?x??3?7x?2x?x?3x??0234234??1?x1?2x2?3x3?x4?1?2x1?x2?x3?x4?1?3x1?2x2?x3?x4?1????3x1?2x2?2x3?3x4?25)?6)?2x1?3x2?x3?x4?1?2x?2x?2x?x?

3、1?5x1?x2?x3?2x4??1234?1?2x?x?x?3x?4234?1??5x1?5x2?2x3?2解1）对方程组得增广矩阵作行初等变换，有?1?1??1??1??1?1?0???0??0??033?2?420000?1521112?3?20?1?4?2?11?1?1200101?1?11010001??1???10??3???0??3??0??1???01??1???20??0???0??0??0?0???037此资料由网络收集而来，如有侵权请告知上传者立即删除。资料共分享，我们负责传递知识。30?5?7?10000?15?3?4?4?400?200?4

4、2358?1200001?1?11010001???2?2??2??2??1???2?0??0?0??因为rank(A)?rank(B)?4?5，所以方程组有无穷多解，其同解方程组为?x1?x4?1??2x1?x5??2，??2x?03???x?x?0?24解得?x1?x?2??x3?x?4??x5?1?k?k?0?k??2?2k其中k为任意常数。2）对方程组德增广矩阵作行初等变换，有?1?1??2??9?1?0?37此资料由网络收集而来，如有侵权请告知上传者立即删除。资料共分享，我们负责传递知识。???0???02?1?3?920?346?31?516?32?32

5、21??1??20????07???25??02????????2?3?7?27120?346?341110?37此资料由网络收集而来，如有侵权请告知上传者立即删除。资料共分享，我们负责传递知识。2?5?2?1631??1?5??16??1??3?34?51?2529?8?011??333?033?2529??72?1?0??334?51?2529?8001?1?333?0000??01?37此资料由网络收集而来，如有侵权请告知上传者立即删除。资料共分享，我们负责传递知识。因为rank(A)?4?rank(A)?3，所以原方程无解。3）对方程组德增广矩阵作行初等变换

6、，有?1?0??1??0?213?73?103?41114??1???30????01????3??0?215?73?1?33?41514???3??3???3??1?0???0??001001?12?4?2108?2??137此资料由网络收集而来，如有侵权请告知上传者立即删除。资料共分享，我们负责传递知识。???30????012????24??0010000200008?8??3?，12??0?因为rank(A)?rank(A)?4，所以方程组有惟一解，且其解为?x1??x2??x3?x?4??8?3?6?0。4）对方程组的增广矩阵作行初等变换，有?3?2??4

7、??7?1?0???0??04?311?27?1717?34?53?131?819?19387??1???22???37此资料由网络收集而来，如有侵权请告知上传者立即删除。资料共分享，我们负责传递知识。?416???3??79??1???200????020????40??07?311?27?1700?83?131?819009???2?16??3?9???20?，0??0?即原方程组德同解方程组为?x1?7x2?8x3?9x4?0，???17x2?19x3?20x4?0由此可解得??x1???x2??x3?x?4??3171917k1?k1?13172017k