行列式练习

内容发布更新时间 : 2024/6/16 11:56:20星期一 下面是文章的全部内容请认真阅读。

?x?y?2z??3?2x?5y?1?4x?5y?0?①?【3,-1】②?【0,0】③?5x?2y?7z?22【1,2,3】 ?3x?7y?2?3x?7y?0?2x?5y?4z?4??bx?ay?2ab?0?④??2cy?3bz?bc?0(a,b,c≠0【-a,b,c】 ?cx?az?0??x1?3x2?6x4?9x?0.5x?0.3x?0.4x?10?1123?2x?x?5x?x?8??1234x2?0.4x1?0.5x3?20【100,80,40】⑤?⑥?【3,-4,-1,1】 ??2x2?x3?2x4??5x?0.2x?0.1x?12312???x1?4x2?7x3?6x4?0?2x1?3x2?11x3?5x4?6?x?x?5x?2x?2?1234⑦?【0,2,0,0】 ?2x1?x2?3x3?4x4?2??x1?x2?3x3?4x4?241、计算下列方程组的系数行列式,并验证所给的数是方程组的解:

?2x1?3x2?4x3?3x4?0?3x?x?11x?13x?0?1234①?,x1?x2?x3?x4?c,c为任意常数 ?4x1?5x2?7x3?2x4?0??13x1?25x2?x3?11x4?0?x1?x2?3x3?x4?3?3x?2x?x?x?5?1234②?,x1?1?c,x2?1?c,x3?0,x4?c,c为任意常数。

5x?5x?2x?1023?1??2x1?3x2?x3?x4?5?2x1?2x2?x3?0?42、判断齐次线性方程组?x1?2x2?4x3?0是否仅有零解。【仅有零解】

?5x?8x?2x?023?1?kx?y?z?0?43、如果齐次线性方程组?x?ky?z?0有非零解,k应取什么值?【4或-1】

?2x?y?z?0??kx?y?z?0?44、k取什么值时,齐次线性方程组?x?ky?z?0仅有零解。【≠1且≠-2】

?2x?y?z?0?B组 1、行列式

k?122k?1?0的充分条件是( )

行列式练习9-6

A.k??1 B.k?3 C.k??1且3 D.k??1或3

k2、行列式22k110=0的充分必要条件是( ) ?112A.k=-2, B.k=3 C. k??2且3 D.k=-2或k=3

?103、若311?2=0。,则?1,?2必须满足( ) 01A. ?1=2,?2=0 B. ?1=?2=2 C. ?1=2,?2可为任意数 D.?1?2均为任意数 4、下列选项中为五级偶排列的是( )A.12435 B.54321 C.32514 D.54231

5、四元素乘积ai1a24a43aj2是四阶行列式值的一项,i,j的取值及该项前应冠以的符号,有下列四种可能情况:①i=3,j=1,前面冠以正号 ②i=3,j=1,前面冠以负号 ③i=1,j=3,前面冠以正号 ④i=1,j=3,前面冠以负号,选项正确的是( ) A. ①③正确 B. ①④正确 C. ②③正确 D. ②④正确 6、下列选项中是五阶行列式中的一项的是( )

A.a12a31a23a45a34 B.?a31a22a43a14a55 C.?a13a21a34a42a51 D.a12a21a55a43a34 7、下列选项中不属于五阶行列式中的一项的是( )

A.a11a23a32a45a54 B.?a51a12a43a34a25 C.?a13a52a34a21a45 D. a55a44a33a22a11

a118、若行列式D?a21a12a22a32a12a22a32a134a112a11?3a122a21?3a222a31?3a323a11?2a123a31?2a32c1a13a23=( ) a334a13?a114a33?a31a31a119、若行列式D?a21a23=1,则行列式D1?4a214a31a33a13a33c1a1a11a31b1b2b3A.-12 B.12 C.-24 D.24

a23,则行列式D1??3a21?9a21?6a22?12a23?3a21=

a31a110、若三阶行列式a2( )A. 12 D B.24 D C.-24 D D.-36 D

2b1?a12b2?a22b3?a3a3c2=6,则行列式a2c3a3c2=( )A.3 B.-3 C.6 D.-6

c3a11a1111、设行列式D?a21a12a22a32a13a?a12211aa,a132333a31a23≠0,且有D1?a21a?222aa33a31a?a3222131行列式练习9-7

a11D2?a21a31a12?2a11a22?2a21a32?2a31a13a11a11?a12a21?a22a31?a32a13a11a12a22a32a12?2a13a22?2a23,则a32?2a33a23,D3?a21a33a31a23,D4?a21a33a31下列选项在判断正确的是( )

A.只有D1=D B.D2=D1=D C.D3=D2=D1=D D。D4=D3=D2=D1=D

000112、设

00a00200100a??1,则a=( )A.-1/2 B.1/2 C.-1 D.1

111?1101?113、n阶行列式110?1=( )A.1 B.-1 C.(?1)n?1 D.(?1)n ????111?0a114、行列式

0a3a500a4a60a200a8中元素a7的代数余子式为( )

00a7A.a2a3a6?a2a4a5 B.a2a4a5?a2a3a6 C.a1a3a6?a2a4a5 D.a3a6a8?a4a5a8

0015、?00??0?00n?a10?=( ) 00n(n?1)2n(n?1)2??a20?an?an?1?0?A. a1a2?an B.(?1)a1a2?an C.(?1)a1a2?an D.(?1)a1a2?an

16、下列n阶行列式中,其值不一定等于-1的是( )

010?00100?00A.

00?0100?10 B.?001?00?????000?10000?01???

01?0010?00行列式练习9-8

100?00010?00C.

100?00001?00 D.

001?00?????000?01000?10a0xb00010?00?????000?10000?01

0y0v?1?1x?1?111?x11x?1?1?1?1,则f(x)=0有( ) A.四个不同的根

=A.abcd-xyuv B.adxv-bcyu C.(ad-bc)(xv-yu) D.(ab-cd)(xy-uv)

17、行列式

0c0d10u1118、设f(x)?1?x B.三个不同的根(其中有一个二重根) C.两个不同的二重根 D.一个四重根。

?2x?ky?c120、如果线性方程组?(c1,c2为不等于零的常数)有唯一解,则k必须满足( )

kx?2y?c?2A.k=0 B.k=-2或k=2 C.k≠-2或k≠2 D. k≠-2且k≠2

21、k=0是20题中方程组有唯一解的( )条件。 A.充分 B.必要 C.充要 D.无关

?2x1?x2?x3?0?23、若齐次线性方程组?x1?kx2?x3?0有非零解,则k必须满足( )

?kx?x?x?0?123A. k=4 B. k=-1 C. k≠-1且k≠4 D. k=-1或k=4 24、若23题中的齐次线性方程组仅有零解,则k必须满足( ) A. k=4 B. k=-1 C. k≠-1且k≠4 D. k=-1或k=4 B组练习参考答案:1.C 2.D 3.C 4.B 5.C 6.D 7.C 8.A 9.B 10.A 11.B 12.A 13.C 14.B 15.D 16. B 17.C 18.D 19.A 20.D 21. A 22.B 23.D 24.C

行列式练习9-9

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