15. are subspaces of F[a, b). a) All functions f in F[a, b] for which f(a) = 0 b) All functions f in F[a, b] for which f(a) = 1 c) All functions f in C[a, b] for which Sa f(x) dx = 0 d) All functions f in D[a, b] for which f'(x) = f(x) e) All functions f in D[a, b] for which f'(x) = e* 4. Determine which of the following sets of n × n ma- trices are subspaces of Mnxn (R). 16. Determi %3D 17. Determi a) The n x n diagonal matrices b) The n x n upper triangular matrices c) The n x n symmetric matrices d) The n x n matrices of determinant zero 18. Determ e) The n x n invertible matrices 5. If A is an m x n matrix and B is a nonzero element of R", do the solutions to the system AX = B form a subspace of R"? Why or why not? 6. Complex numbers a + bi where a and b are integers are called Gaussian integers. Do the Gaussian inte- gers form a subspace of the vector space of complex numbers? Why or why not? 19. Determ 20. Determ Use the sys Maple or an cises 21-2- 7. Do the sequences that converge to zero form a sub- space of the vector space of convergent sequences? How about the sequences that converge to a rational number? 8. Do the series that converge toa positive number form a subspace of the vector space of convergent series? How about the series that converge absolutely? 21. Determ 9. Is in Span 2 3 L.
15. are subspaces of F[a, b). a) All functions f in F[a, b] for which f(a) = 0 b) All functions f in F[a, b] for which f(a) = 1 c) All functions f in C[a, b] for which Sa f(x) dx = 0 d) All functions f in D[a, b] for which f'(x) = f(x) e) All functions f in D[a, b] for which f'(x) = e* 4. Determine which of the following sets of n × n ma- trices are subspaces of Mnxn (R). 16. Determi %3D 17. Determi a) The n x n diagonal matrices b) The n x n upper triangular matrices c) The n x n symmetric matrices d) The n x n matrices of determinant zero 18. Determ e) The n x n invertible matrices 5. If A is an m x n matrix and B is a nonzero element of R", do the solutions to the system AX = B form a subspace of R"? Why or why not? 6. Complex numbers a + bi where a and b are integers are called Gaussian integers. Do the Gaussian inte- gers form a subspace of the vector space of complex numbers? Why or why not? 19. Determ 20. Determ Use the sys Maple or an cises 21-2- 7. Do the sequences that converge to zero form a sub- space of the vector space of convergent sequences? How about the sequences that converge to a rational number? 8. Do the series that converge toa positive number form a subspace of the vector space of convergent series? How about the series that converge absolutely? 21. Determ 9. Is in Span 2 3 L.
Elementary Linear Algebra (MindTap Course List)
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Author:Ron Larson
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Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
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Question
Can you do number 9 show all work ? Vector space
![liñe if
are subspaces of F[a, b].
a) All functions ƒ in F[a, b] for which f (a) = 0
b) All functions f in F[a, b] for which f (a) = 1
c) All functions f in C[a, b] for which
S. f(x) dx = 0
d) All functions f in D[a, b] for which
f'(x) = f(x)
e) All functions f in D[a, b] for which f'(x) = e*
1
16. Determine if
1
1 -
17. Determine if
4. Determine which of the following sets of n × n ma-
trices are subspaces of Mnxn (IR).
1
1
a) The n x n diagonal matrices
b) The n x n upper triangular matrices
c) The n x n symmetric matrices
1
18. Determine if
d) The n x n matrices of determinant zero
e) The n x n invertible matrices
5. If A is an m x n matrix and B
of R", do the solutions to the system AX = B form
a subspace of R"? Why or why not?
6. Complex numbers a + bi where a and b are integers
are called Gaussian integers. Do the Gaussian inte-
gers form a subspace of the vector space of complex
numbers? Why or why not?
a nonzero element
19. Determine if x² –
20. Determine if x³ +.
Use the system of linea
Maple or another apprc
cises 21-24.
7. Do the sequences that converge to zero form a sub-
space of the vector space of convergent sequences?
How about the sequences that converge to a rational
number?
8. Do the series that converge to a positive number form
a subspace of the vector space of convergent series?
How about the series that converge absolutely?
21. Determine if
[]
9. Is
in Span
4
-4
10. Is
-2
in Span
3
-3
1
1
Span
2
11. Is
-5
in Span
3
-3
1
3X
L 372 L3X, 4312](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee22cf2f-b974-4b00-a3cf-09b388e7d65d%2F31c4d504-251b-4c6a-852b-5bd2dc1f7b10%2Fsv6faqq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:liñe if
are subspaces of F[a, b].
a) All functions ƒ in F[a, b] for which f (a) = 0
b) All functions f in F[a, b] for which f (a) = 1
c) All functions f in C[a, b] for which
S. f(x) dx = 0
d) All functions f in D[a, b] for which
f'(x) = f(x)
e) All functions f in D[a, b] for which f'(x) = e*
1
16. Determine if
1
1 -
17. Determine if
4. Determine which of the following sets of n × n ma-
trices are subspaces of Mnxn (IR).
1
1
a) The n x n diagonal matrices
b) The n x n upper triangular matrices
c) The n x n symmetric matrices
1
18. Determine if
d) The n x n matrices of determinant zero
e) The n x n invertible matrices
5. If A is an m x n matrix and B
of R", do the solutions to the system AX = B form
a subspace of R"? Why or why not?
6. Complex numbers a + bi where a and b are integers
are called Gaussian integers. Do the Gaussian inte-
gers form a subspace of the vector space of complex
numbers? Why or why not?
a nonzero element
19. Determine if x² –
20. Determine if x³ +.
Use the system of linea
Maple or another apprc
cises 21-24.
7. Do the sequences that converge to zero form a sub-
space of the vector space of convergent sequences?
How about the sequences that converge to a rational
number?
8. Do the series that converge to a positive number form
a subspace of the vector space of convergent series?
How about the series that converge absolutely?
21. Determine if
[]
9. Is
in Span
4
-4
10. Is
-2
in Span
3
-3
1
1
Span
2
11. Is
-5
in Span
3
-3
1
3X
L 372 L3X, 4312
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