发布时间 : 星期四 文章线性代数(本)习题册行列式 - 习题详解(修改)(加批注)更新完毕开始阅读
系数分别为15，-3.
三、解答题
1.计算下列行列式 .
1234(1)
23413412；
4123解：各行加到第一行，得
1010101011原式=
2341?102334123441234111111 =10012?101?2?1?10000?3?2?10114112
2311112?10?40?160.00?41111112345(2)122324252； 123334353124344454
解：原式=(5-4)(5-3)(5-2)(5-1)(4-3)(4-2)(4-1)(3-2)(3-1) =288.
14916 (3)
4916259162536；
162536491491614916原式=
357957911?35792222?0.
7911132222
0y0x (4)
x0y00x0y；
y0x0xy0x0y原式=?y00y?x0x0 yx0y0x =y2xyy222yx?x2xyx??(x?y).
1xyz (5)1yzx； 1zxy1xyz原式=0y?x?z (y?x) 0z?x?y(z?x)=?(y?x)(z?x)1z1y?(x?y)(y?z)(z?x).1010002?100 (6)31000；
000210000?2
1010 原式=?202?10103100??402000231 =?42?11?3?20. 1?x1111(7)
11?x211111?x31；
1111?x411?1??4000012?11?3
1?x1?x1?x1?x1解：原式=
1x20010x
30100x41?xx11?x?x1x1x??x1?x1?x1203x4=
x200 00x30000x4 =
x1x2x3x4?x2x3x4?x1x3x4?x1x2x4?x1x2x3.
1?5132.设D?11341123，计算A41?A42?A43?A44的值.2234其中A4j(j?1,2,3,4)是D 的代数余子式.
1?513解：A113441?A42?A43?A44?1123?6.
11113?5213. 已知D?110?1?1311,求
M11?M21?M31?M41.2?4?1?1解：M11?M21?M31?M41
=1?M11?(?1)M21?1?M31?(?1)M41
1?521 =
?110?11311=0.
?1?4?1?14.计算下列n阶行列式.
21?1(1)
12?1???； 11?2n?11?111?解：原式=
n?12?112????=(n?1)??n?11?211?11?1 =(n?1)01?0????n?1. 00?1xyy?yyxy?y (2)yyx?y ； ????yyy?x11? 2111?1yxy?y解：原式=?x?(n?1)y?yyx?y ????yyy?x111?10x?y0?0 =?x?(n?1)y?00x?y?0????000?x?y =?x?(n?1)y?(x?y)n?1.
011?11x10?0 (3)10x2?0(xi?0,i?1,2,?,n). ????100?xn