线性代数第二版答案.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。线性代数第二版答案篇一：工程数学线性代数课后同济第五版12345篇二：线性代数第二章答案第二章矩阵及其运算1?已知线性变换???x1?2y1?2y2?y3?x2?3y1?y2?5y3???x3?3y1?2y2?3y3求从变量x1?x2?x3到变量y1?y2?y3的线性变换?解由已知??x1??221??y1??x2???315??y2???x??323??y???2??3???y1??221??x1???7?49??y1??

2、?故y2??315??x2???63?7??y2???y??323??x??32?4?????3????y3??2????y1??7x1?4x2?9x3?y2?6x1?3x2?7x3???y3?3x1?2x2?4x32?已知两个线性变换6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。?1???y1??3z1?z2?x1?2y1?y3?x2??2y1?3y2?2y3??y2?2z1?z3????y3??z2?3z3?x3?4y1?y2?5y3求从z1?z2?z3到x1?x

3、2?x3的线性变换?解由已知?x1??201??y1??201???31?x2????232??y2????232??20?x??415??y??415??0?1??2?????3????613??z1???12?49??z2????10?116??z????3?0??z1?1??z2??z?3???3???x1??6z1?z2?3z3所以有?x2?12z1?4z2?9z3???x3??10z1?z2?16z3?111??123?3?设A??11?1??B???1?24??求3AB?2A及ATB??1?1

4、1??051??????111??123??111?解3AB?2A?3?11?1???1?24??2?11?1??1?11??051??1?11????????058??111???21322??3?0?56??2?11?1????2?1720???290??1?11??429?2????????111??123??058?ATB??11?1???1?24???0?56???1?11??051??290???????4?计算下列乘积?6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

5、责传递知识。?431??7?(1)?1?23??2???570??1??????431??7??4?7?3?2?1?1??35?解?1?23??2???1?7?(?2)?2?3?1???6???570??1??5?7?7?2?0?1??49??????????3?(2)(123)?2???1????3?解(123)?2??(1?3?2?2?3?1)?(10)??1????2?(3)?1?(?12)??3????2?(?1)2?2???24??2?解?1?(?12)??1?(?1)1?2????12???3

6、??3?(?1)3?2???36????????131??0?12?2140??(4)???1?31??1?134?????40?2??131??0?12??6?78?2140??解???1?31???20?5?6??1?134???????40?2??a11a12a13??x1???(5)(x1x2x3)a12a22a23?x2??????aaa?132333??x3?解?a11a12a13??x1???(x1x2x3)a12a22a23?x2?????aaa?132333??x3??x1??(a11x

7、1?a12x2?a13x3a12x1?a22x2?a23x3a13x1?a23x2?a33x3)?x2?6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。?x??3?5?设A??22?a11x12?a22x2?a33x3?2a12x1x2?2a13x1x3?2a23x2x3??1?12??B??1?13???0??问?2??(1)AB?BA吗?解AB?BA?因为AB???3?44??BA??1?36???2??所以AB?BA?8??(2)(A?B)2?A2?2AB?B2吗

8、?解(A?B)2?A2?2AB?B2?因为A?B???2?22??5??2??2?25???2(A?B)2???2?但2???814???1429?5????38??68???1A2?2AB?B2???411???812??3?????0???1016???1527?4????所以(A?B)2?A2?2AB?B2?(3)(A?B)(A?B)?A2?B2吗?解(A?B)(A?B)?A2?B2?因为A?B???2?22??A?B?