大二上期末复习-职协cic线性代数first examination

1、1The First Examination1、A is nn matrix，A=A1 A2 A3，Ai is the ith column of A, so Solution:22、A is 33 matrix,and ,so(a)4, (b)-4, (c)16, (d)-163、A is 33 matrix ，A* is the adjoint matrix of A, and ，please calculate the value of Solution:Solution:34、calculate the determinant of45、if，findSolution:56、67、So

2、lution:78、89、If A and B are nn matrices ，then（ ）A、|-A-1|=- |A-1|-1 B、(AB)K=AKBKC、|A|B|=|B|A| D、|A*|=|A|n-110. If A,B,C, are nn matrices, such that ABC=I，then（ ）A、 ACB=I B、 CAB=I C、 BAC=I D、BCA=I911.If A and B, are nn matrices, then（ ）If A or B is invertible ，so is AB If A or B is not invertible ，the

3、n AB is not invertible(c) If A and B are invertible ，then A+B is invertible (d) If A and B are not invertible, then A+B is not invertible 1012.Suppose,Then （ ） A、AP1P2=B B、 AP2P1=B C、 P1P2A=B D、 P2P1A=B 1113、If Where ai0,i=1,2,n ,find A-112If ，where P is a 33 invertible matrix，then B2004-2A2=1315.If

4、 then 16. supposeIf ，then 123 are independent 1417. Suppose the 3 dimension vectors aredetermine the value of ,which makes the following statement true. （1） is the only combination of 1 2 315(2） could be expressed the linear combination of 1 2 3 ,and the combination is not only.（3） could not be expr

5、essed the linear combination of 1 2 31618. Suppose A=(aij)is 33 matrix,satisfy （1） aij= Aij(i,j=1,2,3),where Aijis the factor of aij（2）a110Please calculate |A|1719.Suppose A is n m matrix, B is m n matrix，and nm，I is n n identity matrix,satisfy AB=I .Show that ：the column vectors of matrix B is independent.1820.Suppose the set 1,2 , ,m-1 (m3) is linear dependent，but the set 2 , ,m is linear independent，discuss： (1) Is 1could be written as the linear combin