大学MOOC Linear Algebra(Beijing Jiaotong University)1463227170 最新慕课完整章节测试答案
Chapter 1-Matrices and Systems of Equations
test1
1、单选题：
Let 
be a system of n linear equations in n unknowns and suppose that 
and 
are both solutions and 
. The system has______solutions.
选项：
A: infinitely many
B: two
C: three
D: finite
答案: 【 infinitely many】
2、单选题：
Let A and B be 10×10 matrices that are partitioned into submatrices as follows
,
.
If 
is a 6 × 5 matrix, and 
is a k × r matrix, in order to make the block multiplication of A times B possible, k is ______ .
选项：
A: 6
B: 5
C: 11
D: 1
答案: 【 5】
3、单选题：
Let A be a 
matrix, then ________.
选项：
A: If Ax=0 has only trivial solution, then Ax=b must have a unique solution.
B: If Ax=0 has a nontrivial solution, then Ax=b must have infinitely many solutions.
C: If Ax=b has a unique solution, then Ax=0 must have a unique solution.
D: If Ax=0 has a nontrivial solution, then 
must have a nontrivial solution.
答案: 【 If Ax=b has a unique solution, then Ax=0 must have a unique solution. 】
4、单选题：
Let AB be all 
square matrices. There must be _______
选项：
A: 
B: AB=BA
C: 
D: 
答案: 【 】
5、单选题：
Let AB be all 
square matrices, if 
, then ______.
选项：
A: AB=I or AB=-I
B: 
C: AB=BA
D: A=B=I
答案: 【 】
6、判断题：
If the row reduced echelon form of A involves free variables, then the system Ax=b will have infinitely many solutions.
选项：
A: 正确
B: 错误
答案: 【 错误】
7、判断题：
Every homogeneous linear system is consistent.
选项：
A: 正确
B: 错误
答案: 【 正确】
8、判断题：
An 
matrix A is nonsingular if and only if the reduced row echelon form of A is I.
选项：
A: 正确
B: 错误
答案: 【 正确】
9、判断题：
If A is nonsingular, then A can be factored into a product of elementary matrices.
选项：
A: 正确
B: 错误
答案: 【 错误】
10、判断题：
If A and B are nonsingular 
matrices, then A+B is also nonsingular and 
.
选项：
A: 正确
B: 错误
答案: 【 错误】
11、判断题：
If 
, then A must be equal to either I or -I.
选项：
A: 正确
B: 错误
答案: 【 错误】
12、判断题：
If A and B are