线性代数第二次测验.doc

江西财经大学 07－08学年第一学期期末考试试卷 试卷代码：12063A 授课课时：48 课程名称：Linear Algebra 适用对象：2006级国际学院 1. Filling In The Blanks (3’×5=15’) (1) = . (2)Let A be (n×n) matrix, if AX=0 has unique solution, then the solution of is . (3)If the system of equations has nonzero solutions, then k= . (4) Let A be (3?) matrix, and -1,2,4 are the eigenvalues of A. Then the eigenvalues of A-1 are . (5) Let . Then the cross product = . 2. There are four choices in each question, but only one is correct. You should choose the correct one into the blank. (3’?=15h’) (1) Let , then x= . A. –2 B. 2 C. -1 D. 1 (2) Let A and B be (n×n) matrices, then . A. AB=0A=0 or B=0 B. AB≠0A≠0 and B≠0 C. AB=0|A|=0 or |B|=0 D. AB≠0|A|≠0 and |B|≠0 (3) Let be a linearly dependent set of vectors, where . Then the number k is . A． -1 B． 1 C． 3 D． -3 (4) Let A be () matrix， then the statement is true. A. If has only solution, then has only solution B. If has only solution，then has only solution C. If has infinitely many solutions，then has infinitely many solutions D. If has no solutions，then has no solutions. (5) If A is (n×n) matrix, are two eigenvalues of A, and are the eigenvectors corresponding to, respectively. Then . A. when , must be proportional B. when, , must be not proportional C. when , must be proportional D. when , must be not proportional 3. (12’) Let , is the cofactor of , Compute: （1）; （2）. 4. (12’) Let the system of linear equations is . Solve this system and express the solutions by vectors. 5. (12’) Let , Compute:, where is the adjoint matrix of . 6. (12’) There are (3×3) matrices A and B such that A+B=AB (1) Show that matrix A-I is invertible, where is an identity matrix; (2) If matrix , Find matrix A. 7. (12’) Find an invertible matrix S, which can make A diagonalizable, where . 8. (10’) Suppose the set of vectors is linear dependent, an