Let 3 = {1, x, x²}, and consider the linear transformation T : P2 (R) → P2 (R) defined by Тр(x)) — Зр(ӕ) + 2p'(ӕ). Given that a (T]8 : d e f h i find the value of the number f.

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

Hi, I need help with this Linear Algebra exercise, please. Thank you!

Let 3 = {1, x, x²}, and consider the linear transformation T : P2 (R) → P2 (R) defined by
Tр(x)) — Зр(г) + 2p'(х). Given that
a
[T]8
d
e f
h i
find the value of the number f.
Transcribed Image Text:Let 3 = {1, x, x²}, and consider the linear transformation T : P2 (R) → P2 (R) defined by Tр(x)) — Зр(г) + 2p'(х). Given that a [T]8 d e f h i find the value of the number f.
Expert Solution
Step 1

Given transformation is T(p(x))=3p(x)+2p'(x)

Given basis is β={1,x,x2}

T(1)=3=3+0.x+0.x2T(x)=3x+2=2+3x+0.x2T(x2)=3x2+2(2x)=3x2+4x=0+4x+3x2

Matrix representation is given by:

TA=320034003

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Propositional Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
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,