[p(-3) Define T: P3 → R¹ by T(p)=P(-1) where P₁ = {a+a₁t+₃²+⣣³ | 㵂 ª₁‚ ª. až are reals } C, [p(3) [1] Show that T is a linear Transformation. Show all support work. [2] Graph the zero vector in Domain of T if there is any. Justify your answer. Also find two vectors in Domain(T) that are scalar multiples if there are any. Justify your answers. [3] Find the matrix for T relative to the basis {1, t, t², t³} for P3, and the standard basis for Rª . Show work to justify your answers. [4] Write the Kernel of Tin form of Span. Show work to justify your answer. [5] Find a non-standard basis for the Range of T. Show work to justify your answer. [6] Given p(t)=-3+4t-7t² +9t³, determine if T(p) is in the Range(T). Show all work to justify your
[p(-3) Define T: P3 → R¹ by T(p)=P(-1) where P₁ = {a+a₁t+₃²+⣣³ | 㵂 ª₁‚ ª. až are reals } C, [p(3) [1] Show that T is a linear Transformation. Show all support work. [2] Graph the zero vector in Domain of T if there is any. Justify your answer. Also find two vectors in Domain(T) that are scalar multiples if there are any. Justify your answers. [3] Find the matrix for T relative to the basis {1, t, t², t³} for P3, and the standard basis for Rª . Show work to justify your answers. [4] Write the Kernel of Tin form of Span. Show work to justify your answer. [5] Find a non-standard basis for the Range of T. Show work to justify your answer. [6] Given p(t)=-3+4t-7t² +9t³, determine if T(p) is in the Range(T). Show all work to justify your
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Kindly solve Q6 in 30 Minutes and get the thumbs up please show neat and clean work for it by hand solution needed
![Define T: P3
R by T(p)=
P(-3)]
P(-1)
p(1)
[p(3)
where P₁ = {a+at+a₂t² +α₂t³ | α₁ α₁₁ a₂. a3 are reals }
[1] Show that T is a linear Transformation. Show all support work.
[2] Graph the zero vector in Domain of T if there is any. Justify your answer.
Also find two vectors in Domain(T) that are scalar multiples if there are any. Justify your answers.
[3] Find the matrix for T relative to the basis {1, t, t², t³} for P3, and the standard basis for Rª. .
Show work to justify your answers.
[4] Write the Kernel of T in form of Span. Show work to justify your answer.
[5] Find a non-standard basis for the Range of T. Show work to justify your answer.
[6] Given p(t)=-3+4t-7t² +9t³, determine if T(p) is in the Range(T). Show all work to justify your](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e9c2f78-47b3-4241-a668-8f909847ed46%2Fa9566277-1a9c-41d0-93d6-70186e5eefaa%2Fpkfxcxa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Define T: P3
R by T(p)=
P(-3)]
P(-1)
p(1)
[p(3)
where P₁ = {a+at+a₂t² +α₂t³ | α₁ α₁₁ a₂. a3 are reals }
[1] Show that T is a linear Transformation. Show all support work.
[2] Graph the zero vector in Domain of T if there is any. Justify your answer.
Also find two vectors in Domain(T) that are scalar multiples if there are any. Justify your answers.
[3] Find the matrix for T relative to the basis {1, t, t², t³} for P3, and the standard basis for Rª. .
Show work to justify your answers.
[4] Write the Kernel of T in form of Span. Show work to justify your answer.
[5] Find a non-standard basis for the Range of T. Show work to justify your answer.
[6] Given p(t)=-3+4t-7t² +9t³, determine if T(p) is in the Range(T). Show all work to justify your
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