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Chapter 1 Systems of Linear Equations unit test 1
1、
A:
B:
C:
D:
答案:
2、
In the following matrices, ( ) is not elementary matrices.
A:
B:
C:
D:
答案:
3、
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、
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、
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、
A:
B:
C:
D:
答案:
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、
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) = .
答案: 1.25
10、
答案: 10
Chapter 3 Vector Space unit test 3
1、
A:
1,1.
B:
2,2.
C:
2,1.
D:
1,2.
答案:
1,1.</span>】
2、
Let A be an m×n matrix, then ( ).
A:
AAT =ATA.
B:
if rank(A) = m, then AT A is invertible.
C:
if rank(A) = n, then AAT is invertible.
D:
if rank(A) = n, then AT A is invertible.
答案:
if rank(A) = n, then AT A is invertible.</span>】
3、
Let A be an 10 × 6 matrix, and rank(A) = 3, then
we have ( ).
A:
rank(AT ) = 6.
B:
dim(N(AT )) = 6.
C:
dim(N(A)) = 3.
D:
dim(N(AT )) = 3.
答案:
dim(N(A)) = 3.</span>】
4、
If x1, x2, ..., xn span Rn, then they are linearly independent.
A:正确
B:错误
答案: 正确
5、
If A is an m × n matrix, then A and AT have the same
rank.
A:正确
B:错误
答案: 正确
6、
If U is the reduced row echelon form of A, then A and U have the same row space.
A:正确
B:错误
答案: 正确
7、
Determine whether the set {(x1, x2)T |x1 + x2 = 0} form subpace of R2 (Yes/No)
答案: Yes
8、
答案: 1
9、
答案: (5,9) (1,4)
10、
答案: 1 0 1 0 2
0 1 2 0 -1
0 0 0 1 3
0 0 0 0 0
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