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1、线性代数(经管类)(课程代码04184)第一大题:单项选择题1、设行列式=1 , =2, 则= (D ) Error! Reference source not found.A.3 Error! Reference source not found.B.1 Error! Reference source not found.C.1 Error! Reference source not found.D.32、 设A为3阶方阵,且已知|-2A|=2,则|A|=(B ) Error! Reference source not found.A.1 Error! Reference source no
2、t found.B. Error! Reference source not found.C. Error! Reference source not found.D.13、设矩阵A,B,C为同阶方阵,则=_B_ Error! Reference source not found.A. Error! Reference source not found.B. Error! Reference source not found.C. Error! Reference source not found.D.4、设A为2阶可逆矩阵,且已知 = ,则A=(D) Error! Reference sou
3、rce not found.A. Error! Reference source not found.B. Error! Reference source not found.C. Error! Reference source not found.D.5、设A为mn矩阵,则齐次线性方程组=0仅有零解的充分必要条件是(A) Error! Reference source not found.A.A的列向量组线性无关 Error! Reference source not found.B.A的列向量组线性相关 Error! Reference source not found.C.A的行向量组线
4、性无关 Error! Reference source not found.D.A的行向量组线性相关6、已知,是非齐次线性方程组=b的两个不同的解,是其导出组=0的一个基础解系,为任意常数,则方程组=b的通解可以表为(A) Error! Reference source not found.A. Error! Reference source not found.B. Error! Reference source not found.C. Error! Reference source not found.D.7、设3阶矩阵A与B相似,且已知A的特征值为2,2,3 则 |= (A ) Err
5、or! Reference source not found.A. Error! Reference source not found.B. Error! Reference source not found.C.7 Error! Reference source not found.D.128、设A为3阶矩阵,且已知|3A+2E|=0,则A必有一个特征值为(A ) Error! Reference source not found.A. Error! Reference source not found.B. Error! Reference source not found.C. Erro
6、r! Reference source not found.D.9、二次型 的矩阵为(C ) Error! Reference source not found.A. Error! Reference source not found.B. Error! Reference source not found.C. Error! Reference source not found.D.10、设A为三阶方阵且|A|=-2,则 (D) Error! Reference source not found.A.108 Error! Reference source not found.B.12 Err
7、or! Reference source not found.C.12 Error! Reference source not found.D.10811、如果方程组 有非零解,则 k=(B ) Error! Reference source not found.A.2 Error! Reference source not found.B.1 Error! Reference source not found.C.1 Error! Reference source not found.D.212、设A、B为同阶方阵,下列等式中恒正确的是(D) Error! Reference source
8、not found.A.AB=BA Error! Reference source not found.B. Error! Reference source not found.C. Error! Reference source not found.D.13、设A为四阶矩阵,且 |A|=2 则 (C) Error! Reference source not found.A.2 Error! Reference source not found.B.4 Error! Reference source not found.C.8 Error! Reference source not found
9、.D.1214、设 可由向量 =(1,0,0)=(0,0,1)线性表示,则下列向量中 只能是(B ) Error! Reference source not found.A.(2,1,1) Error! Reference source not found.B.(3,0,2) Error! Reference source not found.C.(1,1,0) Error! Reference source not found.D.(0, 1,0)15、向量组的秩不为S()的充分必要条件是(C ) Error! Reference source not found.A.全是非零向量 Erro
10、r! Reference source not found.B.全是零向量 Error! Reference source not found.C.中至少有一个向量可以由其它向量线性表出 Error! Reference source not found.D.中至少有一个零向量16、设A为矩阵,方程=0仅有零解的充分必要条件是(C) Error! Reference source not found.A.的行向量组线性无关 Error! Reference source not found.B.A的行向量组线性相关 Error! Reference source not found.C.A的列
11、向量组线性无关 Error! Reference source not found.D.A的列向量组线性相关17、设A与B是两个相似 n 阶矩阵,则下列说法错误的是(D) Error! Reference source not found.A.|A|=|B| Error! Reference source not found.B.秩(A)=秩(B) Error! Reference source not found.C.存在可逆阵P,使P1AP=B Error! Reference source not found.D.E-A = E- B18、与矩阵A= 相似的是(A ) Error! Re
12、ference source not found.A. Error! Reference source not found.B. Error! Reference source not found.C. Error! Reference source not found.D.19、设有二次型 则 (C ) Error! Reference source not found.A.正定 Error! Reference source not found.B.负定 Error! Reference source not found.C.不定 Error! Reference source not f
13、ound.D.半正定20、设行列式D= =3,D1= ,则D1的值为(C) Error! Reference source not found.A.15 Error! Reference source not found.B.6 Error! Reference source not found.C.6 Error! Reference source not found.D.1521、设矩阵 = ,则(C) Error! Reference source not found.A.a=3,b= -1,c=1,d=3 Error! Reference source not found.B.a= -
14、1,b=3,c=1,d=3 Error! Reference source not found.C.a=3,b= -1,c=0,d=3 Error! Reference source not found.D.a= -1,b=3,c=0,d=322、设3阶方阵A的秩为2,则与A等价的矩阵为(B) Error! Reference source not found.A. Error! Reference source not found.B. Error! Reference source not found.C. Error! Reference source not found.D.23、设A
15、为n阶方阵,n2,则 |-5A| =(D) Error! Reference source not found.A. Error! Reference source not found.B.-5|A| Error! Reference source not found.C.5|A| Error! Reference source not found.D.24、设A=,则 =(B ) Error! Reference source not found.A.-4 Error! Reference source not found.B.-2 Error! Reference source not found.C.2 Error! Reference source not found.D.425、向量组,(