n. Justify your answers, 5. All polynomials of the form p(t) = at² , where a is in R. %3D 6. All polynomials of the form p(t) = a +t², where a is in R. 7. All polynomials of degree at most 3, with integers as coeffi- cients. 8. All polynomials in P, such that p(0) = 0. %3D 9. Let H be the set of all yectors of L17-
n. Justify your answers, 5. All polynomials of the form p(t) = at² , where a is in R. %3D 6. All polynomials of the form p(t) = a +t², where a is in R. 7. All polynomials of degree at most 3, with integers as coeffi- cients. 8. All polynomials in P, such that p(0) = 0. %3D 9. Let H be the set of all yectors of L17-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Topic Video
Question
Number 6 and 8 please ?
![15.
vectors or a vector and a scalar-to
show that H is not a subspace of R2.
4. Construct a geometric figure that illustrates why a line in R?
not through the origin is not closed under vector addition.
17.
In Exercises 5-8, determine if the given set is a subspace of P, for
an appropriate value of n. Justify your answers,
19. If a mass m 1
pulled downwad
begin to oscillate
resting position i g
5. All polynomials of the form p(t)
= at?, where a is in R.
6. All polynomials of the form p(t) = a +t², where a is in R.
7. All polynomials of degree at most 3, with integers as coefi-
cients.
y(t) = C cos ot +
where o is a constas
(See the figure bel
described in (5) (w
8. All polynomials in P, such that p(0) = 0.
-21
space.
9. Let H be the set of all vectors of the form
Find a
vector v in R³ such that H = Span {v}. Why does this show
that H is a subspace of R3?
10. Let H be the set of all vectors of the form
, where t
is any real number. Show that H is a subspace of R3. (Use
the method of Exercise 9.)
2b +3c
9-
2c
11. Let W be the set of all vectors of the form
where b andc are arbitrary. Find vectors u and v such that
W Span {u, v}. Why does this show that W is a subspace
of R³?
20. The set of all cont
closed interval [a,
a subspace of the
defined on [a, b].
2s+4t
a. What facts abc
in order to derr
2s
12. Let W be the set of all vectors of the form
2s - 3t
as claimed?
calculus class.)
Show that W is a subspace of R. (Use the method of
Exercise 11.)
b. Show that { in
Cla, b).
13. Let v1 =
= EA
2, and w =
For fixed positive integ
matrices is a vector spac
of matrices and multiplia
,V2
2.
a. Is w in {v1, V2, V3}? How many vectors are in {v1, V2, V3}?
b. How many vectors are in Span {v1, V2, V3}?
c. Is w in the subspace spanned by {V1, V2, V3}? Why?
21. Determine if the set
is a subspace of M
14. Let v1, V2, V3 be as in Exercise 13, and let](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee22cf2f-b974-4b00-a3cf-09b388e7d65d%2Fa2eaaafa-212f-4da2-ab07-edc8740d49a6%2F2a1yjbc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:15.
vectors or a vector and a scalar-to
show that H is not a subspace of R2.
4. Construct a geometric figure that illustrates why a line in R?
not through the origin is not closed under vector addition.
17.
In Exercises 5-8, determine if the given set is a subspace of P, for
an appropriate value of n. Justify your answers,
19. If a mass m 1
pulled downwad
begin to oscillate
resting position i g
5. All polynomials of the form p(t)
= at?, where a is in R.
6. All polynomials of the form p(t) = a +t², where a is in R.
7. All polynomials of degree at most 3, with integers as coefi-
cients.
y(t) = C cos ot +
where o is a constas
(See the figure bel
described in (5) (w
8. All polynomials in P, such that p(0) = 0.
-21
space.
9. Let H be the set of all vectors of the form
Find a
vector v in R³ such that H = Span {v}. Why does this show
that H is a subspace of R3?
10. Let H be the set of all vectors of the form
, where t
is any real number. Show that H is a subspace of R3. (Use
the method of Exercise 9.)
2b +3c
9-
2c
11. Let W be the set of all vectors of the form
where b andc are arbitrary. Find vectors u and v such that
W Span {u, v}. Why does this show that W is a subspace
of R³?
20. The set of all cont
closed interval [a,
a subspace of the
defined on [a, b].
2s+4t
a. What facts abc
in order to derr
2s
12. Let W be the set of all vectors of the form
2s - 3t
as claimed?
calculus class.)
Show that W is a subspace of R. (Use the method of
Exercise 11.)
b. Show that { in
Cla, b).
13. Let v1 =
= EA
2, and w =
For fixed positive integ
matrices is a vector spac
of matrices and multiplia
,V2
2.
a. Is w in {v1, V2, V3}? How many vectors are in {v1, V2, V3}?
b. How many vectors are in Span {v1, V2, V3}?
c. Is w in the subspace spanned by {V1, V2, V3}? Why?
21. Determine if the set
is a subspace of M
14. Let v1, V2, V3 be as in Exercise 13, and let
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