Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(d) Hence, find a basis for the kernel of T expressed as linear combinations of the vectors V₁,..., V5 and state the dimension of the kernel, Ker(T), of T.

(d) Hence, find a basis for the kernel of T expressed as linear combinations of the vectors V₁,..., V5 and state the dimension of the kernel, Ker(T), of T.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

answer the question d,please.

2. Let T: P₁(R) → R2 be the map given by T()=(f(1),f"(1)) where P₁ (R) is the set of polynomials of degree 4 or less and f"" (1) is the evaluation of d³f\ the third derivative of f at 1, i.e., dx³ (a) Show that I is a linear map. (b) Show that the set (c) Calculate the matrix representing T with respect to the standard basis e₁ = = (1,0)¹, e₂ = (0, 1)¹ of R² and the basis {V₁, V2, V3, V4, V5} of P₁ (R). (d) Hence, find a basis for the kernel of T expressed as linear combinations of the vectors V₁,..., v5 and state the dimension of the kernel, Ker(T), of T. (e) Find a basis for the image of T, Im(T), and state its dimension.
Transcribed Image Text:2. Let T: P₁(R) → R2 be the map given by T()=(f(1),f"(1)) where P₁ (R) is the set of polynomials of degree 4 or less and f"" (1) is the evaluation of d³f\ the third derivative of f at 1, i.e., dx³ (a) Show that I is a linear map. (b) Show that the set (c) Calculate the matrix representing T with respect to the standard basis e₁ = = (1,0)¹, e₂ = (0, 1)¹ of R² and the basis {V₁, V2, V3, V4, V5} of P₁ (R). (d) Hence, find a basis for the kernel of T expressed as linear combinations of the vectors V₁,..., v5 and state the dimension of the kernel, Ker(T), of T. (e) Find a basis for the image of T, Im(T), and state its dimension.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS