线性代数英文试卷(习题)

ZheJiang University Of Science And Technology Civil Engineering 14 Final Test

Linear Algebra Final Test(15.06)

Cautions:[1]You are allowed to finish this test within 60 minutes.

[2]Fill the answer in the question paper in part.1 1.Filling Blanks(45 points) 姓名：x[1]figure out the value of the following determinant A=

xyxyxyxy______________

xyy学号：班级： 32T102[2]Here are two matrix,A01,B01014T,please find AB=____________,BA=______________.

[3]A known matrix B satisfies the following equation,B2-B-2E=0,if B,B+2E are nonsingular,thus (B+2E)-1=___________ [4]Pick up the vectors which are linearly independent__________ ①(-2,1)T,(1,3)T,(2,4)T ②2,x2,x,2x+3

③x+2,x+1,x2-1

④(1,2)T,(-1,1)T

122[5]A4t3.if B is a nonzero 3x3 matrix,AB=0,thus t=________ 311OA[6]|A|=|B|=|C|=2,and they’re all 3*3 matrix,find the value of D=2(B)1C=____________

3[7]Judge whether 200253A052，B050 have the same eigenvalues______(‘Y’OR’N’),if yes,please find 004004 them=_____________[8]find matrix X,which satisfies the equation

1121,X=___________

X241250[9]find the eigenvectors of A=18

,______________________2.Solve problems(55 points) [1]A,B are 3x3 matrix,and they satisfy the equation

AB2AB，and

002B040，findAE.

200[2]If 12A，find a matrix U21，making U1AU exist.(Tip:is a diagonal matrix). ZheJiang University Of Science And Technology Civil Engineering 14 Final Test

2x1x2x3x413[3]The equation is3x12x2x33x44,find its general solution;

[4]A=4x4x3x5x2023410430000100find 041A1 and A*.1111[5]0is one of eigenvectors of matrixAm11， 111n（1）find the eigenvalue α,then figure out the value of m,n；

（2）Judge whether matrix A can be diagonalizable;if yes,please find a matrix diagonal matrix).

U,making U1AU exist.(Tip:is a

11111[6]The array of vectors β,α are given,10,2m,31 ,11,22 .They have the same rank of

1320nmatrix,meanwhile,3is linearly independent with1,2，find the value of

m,n.----------------Draft paper Area------------- ZheJiang University Of Science And Technology Civil Engineering 14 Final Test

Answer of Liner Algebra(2015.06)

3.-0.25(A-3E)

4.[4]

5.t=-3 1.Filling blanks(each question with 5 marks) 1.2xy(x+y)

301502.AB,BA214

1016026.27/8

7.Y 2,5,4

8.X0.50 1.51

9.(-3,1)T,(0,1)T 2.Solve questions(each question with 8-10 marks) 1.A-E=2(B-2E)-1(FIND THE EXACT ANSWER BY YOURSELF)

16000157513.Xα07β

77004900772.U=0.50

11

4.C1AO1O-1

A*=|A|xA 1B

5.[1]Eigenvalue is 2,m=n=1 6.M=2,n=1

[2]U consists of 3 eigenvectors whose eigenvalue are 1.2.-2

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