Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分

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Chapter 1 Systems of Linear Equations unit test 1

1、 Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第1张

A:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第2张
B:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第3张
C:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第4张
D:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第5张
答案: Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第3张

2、

                In the following matrices, (  ) is not elementary matrices.

A:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第7张
B:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第8张
C:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第9张
D:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第10张
答案: Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第8张

3、 Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第12张

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 interchang-

ing the first and second columns.
D:

                the elementary column operation of interchang-

ing the second and third columns.
答案:

                the elementary row operation of interchanging

the second and third rows.

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

A:正确
B:错误
答案: 正确

5、

                If A is a 3×3 matrix and a1 +2a2 −a3 = 0, then A must be singular.

A:正确
B:错误
答案: 正确

6、

                If A and B are n×n matrices, then (A−B)2 =A2−2AB+B2.

A:正确
B:错误
答案: 正确

7、

                Use back substitution to solve the following systems

of equations:

    <img src="http://edu-image.nosdn.127.net/3C4C3AE6C1AB2BC14E8AAF46F9DEF525.jpg?imageView&thumbnail=890x0&quality=100"    />

答案: 4, 1, 3

8、 Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第13张
答案: -2/3

9、 Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第14张
答案: 5 -10 15
5 -1 4
8 -9 6

10、 Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第15张
答案: 1 2 -3
-1 1 -1
0 -2 3

Chapter 2 Determinants unit test 2

1、 Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第16张

A:1.
B:6.
C:-6.
D:0.
答案: -6.

2、

                Let A be a n×n matrix, then ( ).

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).</span>

3、 Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第17张

A:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第18张
B:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第19张
C:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第20张
D:Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第21张
答案: Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第21张

4、

                det(A+B)=det(A)+det(B).

A:正确
B:错误
答案: 错误

5、

                A triangular matrix is nonsingular if and only if its

diagonal entries are all nonzero.

A:正确
B:错误
答案: 正确

6、

                If A and B are row equivalent matrices, then their

determinants are equal.

A:正确
B:错误
答案: 错误

7、 Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第23张
答案: -8 8

8、 Linear Algebra(Northwestern Polytechnical University) 中国大学慕课答案2024完整版100分第24张
答案: -1 6

9、

                Let A and B be 3×3 matrices with det(A) = 4 and det(B) = 5. Find the value of det (A−1 B) =             .

       


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