. .. . .
线性代数课后习题参考答案(初稿)
习题一
1. 用行列式定义计算下列各题 (1)
?4235??4?5?3?2??26
011(2)101?(?1)1?211000101110?(?1)1?3?2 1011(3)
020030000004100036002045020?(?1)1?3300?2?(?1)1?200402?(?1)1?13004??24
36?2?(?1)1?2(4)
4546789108910810?3?(?1)1?34589?4
2. 利用行列式的性质计算下列各题
2120413214150622325062?0
3?12115(1)
2?162(2)
211890?50?71?626?2189?501?62?10?513???51?1?2?1?10?2510300?5?10?5?12???5?11?3??108
0?9?712?abac?cdcfae?ef?bbc?cce?e?111?1111
?1(3)bdbfde?adfbe?adfbce1. . . w
. .. . .
?111?adfbce0002?4adfbce 20a?00b0ba?b0b00??a(a?b)3abbb(4)
ababaababbba11a?bb?aa?b?10??a(a?b)3
b?ab?a(5)
xaaaxaaaxaaaax?(n?1)aaaa1aaaaa xax?(n?1)axaa=x?(n?1)aaxx10x?(n?1)aaa00x?a0000x?a?[x?(n?1)a](x?a)n?1
a1xaa =[x?(n?1)a]1axx1aa1x?a=[x?(n?1)a]1010(6)
a2b2cd22(a?1)2(b?1)2(c?1)(d?1)22(a?2)2(b?2)2(c?2)(d?2)22(a?3)2(b?3)2(c?3)(d?3)22?a2b2cd222a?12a?32a?52b?12b?32b?52c?12c?32c?52d?12d?32d?5?0
(7)
11112222332?333n?1n?1n?1n?2?n?1n?1nnnnn?1?n?100110102100100000n?200000n?1?(n?1)!
11?2
. . . w
. .. . .
(8)
012n?1?1111?100101n?2?1?111?1?20210n?3??1?1?11??1?2?2n?1n?2n?30n?1n?2n?30n?12n?32n?4?(?1)n?12n?2(n?1)
3. 证明下列各题
a1?b1b1?c1c1?a1a1b1?c1c1?a1b1b1?c1c1?a1(1)a2?b2b2?c2c2?a2?a2b2?c2c2?a2?b2b2?c2c2?a2
a3?b3b3?c3c3?a3a3b3?c3c3?a3b3b3?c3c3?a3a1b1?c1c1b1c1c1?a1a1b1c1b1c1a1?a2b2?c2c2?b2c2c2?a2?a2b2c2?b2c2a2 a3b3?c3c3b3c3c3?a3a3b3c3b3c3a3a1b1c1?2a2b2c2 a3b3c30xyz(2)
x0zyyz0x??(x?y?z)(y?z?x)(z?x?y)(x?y?z)(证明略)
zyx01?x1111111x111(3)
11?x1111?x1101?x11111?y1?111?y1?011?y1
1111?y1111?y0111?y1000?1?x001?x11?111?x110y0?x11?y1?xy2?x??11?y1?01?y1000?y111?y??111?y01?100? ?xy2?x??0y0?x1?y1??xy2?xy2?x2y2?22?11??xy ?00?yy??. . . w
000n?11?1???y??1
线性代数课后练习参考答案(初稿)
![](/skin/haowen/images/icon_star.png)
![](/skin/haowen/images/icon_star.png)
![](/skin/haowen/images/icon_star.png)
![](/skin/haowen/images/icon_star.png)