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 byTр(x)) — Зр(г) + 2p'(х). Given thata[T]8de fh ifind the value of the number f.

Name: Hi, I need help with this Linear Algebra exercise, please. Thank you!
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Description: 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 byTр(x)) — Зр(г) + 2p'(х). Given thata[T]8de fh ifind the value of the number f.

Answered: Let 3 = {1, x, x²}, and consider the…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 16CM

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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.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

Expert Solution

Step 1

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

Given basis is $β = {1, x, x^{2}}$

$T (1) = 3 = 3 + 0 . x + 0 . x^{2} T (x) = 3 x + 2 = 2 + 3 x + 0 . x^{2} T (x^{2}) = 3 x^{2} + 2 (2 x) = 3 x^{2} + 4 x = 0 + 4 x + 3 x^{2}$

Matrix representation is given by:

$T_{A} = [\begin{matrix} 3 & 2 & 0 \\ 0 & 3 & 4 \\ 0 & 0 & 3 \end{matrix}]$

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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.