Chapter1SystemsofLinearEquations

unittest1

1、单选题:

​选项:
A:
B:
C:
D:
答案: 【 

2、单选题:

‏​
‏​
‏​ In the following matrices, ( ) is not elementary matrix.‏​
‏​
‏​
‏​‏
选项:
A:
B:
C:
D:
答案: 【 

3、单选题:

​选项:
A:

the elementary row operation of interchanging
the first and second rows.

B:

the elementary row operation of interchanging
the second and third rows.

C:

the elementary column operation of interchanging the first and second columns.

D:

the elementary column operation of interchanging the second and third columns.

答案: 【 

the elementary row operation of interchanging
the second and third rows.

4、判断题:

If  is nonsingular, then can be factored into a
product of elementary matrices.

​选项:
A: 正确
B: 错误
答案: 【 正确

5、判断题:

‏‍
‏‍
‏‍If A is a 3×3 matrix and a1 +2a2 −a3 = 0, then A must be singular.‏‍
‏‍
‏‍
‏‍‏
选项:
A: 正确
B: 错误
答案: 【 正确

6、判断题:

‏‏
‏‏
‏‏If A and B are n×n matrices, then (A-B)2 = A2 −2AB+B2.‏‏
‏‏
‏‏
‏‏‏
选项:
A: 正确
B: 错误
答案: 【 正确

7、填空题:

Use back substitution to solve the following systems
of equations:

‌答案: 【 x1 = 4
x2 = 1
x3 = 3

8、填空题:

​答案: 【 - 2/3

9、填空题:

​答案: 【 5 -10 15
5 -1 4
8 -9 6

10、填空题:

‎答案: 【 1 2 -3
-1 1 -1
0 -2 3

Chapter2Determinants

unittest2

1、单选题:

‌选项:
A: 1
B: 6
C: -6
D: 0
答案: 【 -6

2、单选题:

‎‍
‎‍
‎‍Let A be a n×n matrix, then (  )‎
选项:
A:

AAT =ATA.
B:

det(AAT ) = det(AT A).
C:

if det(A) = 0, then A is invertible.
D:

if det(A) = 0, then AT is invertible.
答案: 【 

det(AAT ) = det(AT A).】

3、单选题:

‎选项:
A:

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