文档介绍：线性代数第二版答案
篇一：工程数学线性代数课后答案 同济第五版
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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???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?4x3
2? 已知两个线性变换 ?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? x2? 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?11??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?
?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??