Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Number 4 part a b c d and e
![13. Is 3x² in Span(x?
14. Is sin(x +I|4)n Spanl
3. Determine which of the following sets of functions
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*
15. Determine if
16. Determine if
%3D
4. Determine which of the following sets of n x n ma-
trices are subspaces of Mnxn (R).
17. Determine if
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. Determine if
0 1
e) The n x n invertible matrices
-1 0
5. If A is an m x n matrix and B is a nonzero element
of Rm, do the solutions to the system AX = B form
a subspace of R"? Why or why not?
19. Determine if x² - 1,
20. Determine if x'+x,:
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?
Use the system of linear ec
Maple or another appropri
cises 21-24.
1. 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?
1
21. Determine if
-1
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?
4
-1
9. Is
in Span
-4
10. Is
in Span 31[ -41 [ 2 1.](https://content.bartleby.com/qna-images/question/ee22cf2f-b974-4b00-a3cf-09b388e7d65d/433d7b97-cebc-425e-961a-0a187e44861c/jzlf3hra_processed.jpeg)
Transcribed Image Text:13. Is 3x² in Span(x?
14. Is sin(x +I|4)n Spanl
3. Determine which of the following sets of functions
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*
15. Determine if
16. Determine if
%3D
4. Determine which of the following sets of n x n ma-
trices are subspaces of Mnxn (R).
17. Determine if
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. Determine if
0 1
e) The n x n invertible matrices
-1 0
5. If A is an m x n matrix and B is a nonzero element
of Rm, do the solutions to the system AX = B form
a subspace of R"? Why or why not?
19. Determine if x² - 1,
20. Determine if x'+x,:
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?
Use the system of linear ec
Maple or another appropri
cises 21-24.
1. 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?
1
21. Determine if
-1
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?
4
-1
9. Is
in Span
-4
10. Is
in Span 31[ -41 [ 2 1.
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