[1] Given the homomorphism p: P4 - R3 defined by [b + c] p(a + bx + cx2 + dx3 + ex4) = d La Find the Range Space of p,R(p), and the Null Space p, N(9),which is also known as the kernel of o, denoted ker(p) or Kq. • Simplif y those sets as much as possible. Find bases for the domain of p, R(9), and N(p) or Kg. Then, find dimension of the domain of q,the Rank of o and Nullity of q. Finally, check those three values by using a result from class. Null(o) = Basis for N(o) Nullity(9) = Range(q) = Basis for R(p) Rank(4) = Basis for the Domain of e Dim(Domain) = Check your results:
[1] Given the homomorphism p: P4 - R3 defined by [b + c] p(a + bx + cx2 + dx3 + ex4) = d La Find the Range Space of p,R(p), and the Null Space p, N(9),which is also known as the kernel of o, denoted ker(p) or Kq. • Simplif y those sets as much as possible. Find bases for the domain of p, R(9), and N(p) or Kg. Then, find dimension of the domain of q,the Rank of o and Nullity of q. Finally, check those three values by using a result from class. Null(o) = Basis for N(o) Nullity(9) = Range(q) = Basis for R(p) Rank(4) = Basis for the Domain of e Dim(Domain) = Check your results:
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
Question
![I.
In this section, find the required spaces, bases, and values.
[1] Given the homomorphism p: P → R³ defined by
[b +c]
o(a + bx + cx2 + dx³ + ex*) =
d
La
el
Find the Range Space of o,R(9), and the Null Space o, N(9),which is also known as
the kernel of o, denoted ker(4) or Kp.
• Simplify those sets as much as
Find bases for the domain of p, R(4), and N(p) or Kg.
possible.
Then, find dimension of the domain of 9, the Rank of o and Nullity of y.
Finally, check those three values by using a result from class.
Null(o) =
Basis for N(o)
Nullity(9) =
Range(o) =
Basis for R(o)
Rank(4) =
Basis for the Domain of o
Dim(Domain)
Check your results:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa9a9ea7-0a60-40f2-88c8-00f846edd995%2F3cfd2812-2b07-4f0c-9a2d-985279f84f27%2F2lp7mg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:I.
In this section, find the required spaces, bases, and values.
[1] Given the homomorphism p: P → R³ defined by
[b +c]
o(a + bx + cx2 + dx³ + ex*) =
d
La
el
Find the Range Space of o,R(9), and the Null Space o, N(9),which is also known as
the kernel of o, denoted ker(4) or Kp.
• Simplify those sets as much as
Find bases for the domain of p, R(4), and N(p) or Kg.
possible.
Then, find dimension of the domain of 9, the Rank of o and Nullity of y.
Finally, check those three values by using a result from class.
Null(o) =
Basis for N(o)
Nullity(9) =
Range(o) =
Basis for R(o)
Rank(4) =
Basis for the Domain of o
Dim(Domain)
Check your results:
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