Linear Algebra(Northwestern Polytechnical University) 中国大学MOOC答案2024版100分完整版

Chapter 1 Systems of Linear Equations unit test 1

1、

答案:

2、

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

答案:

3、

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.

答案: 正确

5、

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

答案: 正确

6、

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

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、
答案: -2/3

9、
答案: 5 -10 15
5 -1 4
8 -9 6

10、
答案: 1 2 -3
-1 1 -1
0 -2 3

Chapter 2 Determinants unit test 2

1、

答案: -6.

2、

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

答案:

                det(AAT ) = det(AT A).</span>

3、

答案:

4、

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

答案: 错误

5、

                A triangular matrix is nonsingular if and only if its

diagonal entries are all nonzero.

答案: 正确

6、

                If A and B are row equivalent matrices, then their

determinants are equal.

答案: 错误

7、
答案: -8 8

8、
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) =             .

                1,1.</span>

                Let A be an m×n matrix, then ( ).

                 if rank(A) = n, then AT A is invertible.</span>

                Let A be an 10 × 6 matrix, and rank(A) = 3, then

                dim(N(A)) = 3.</span>

                If x1, x2, ..., xn span Rn, then they are linearly independent.

                If A is an m × n matrix, then A and AT have the same

                If U is the reduced row echelon form of A, then A and U have the same row space.

                Determine whether the set {(x1, x2)T |x1 + x2 = 0} form subpace of R2   (Yes/No)