2. Determine whether Tis a linear transformation (by proving or by giving counterexample) where Pzis a vector space of polynomials of highest degree 2 with standard operations and Ma-2 is a vector space of matrices of size 2x2 with standard operations. a. T: P» Pa T(ax? + bx + c) = a(x + 1)² + b(x + 1) +c b. T: P Pa T(ax? + bx + c) = (a + 1)x² + (b + 1)x + (e + 1) c. T: Maa P: T( )= ar + cx-2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 20EQ
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2. Determine whether Tis a linear transformation (by proving or by giving counterexample) where
Pz is a vector space of polynomials of highest degree 2 with standard operations and M2-2 is a
vector space of matrices of size 2x2 with standard operations.
a. T: P:» P2
T(ax? + bx + c) = a(x + 1)? + b(x + 1) +c
b. T: P:» P:
T(ax² + bx + c) = (a + 1)x² + (b + 1)x + (e + 1)
c. T: Ma2 P2
T(: ) = ax + cx - 2
Transcribed Image Text:2. Determine whether Tis a linear transformation (by proving or by giving counterexample) where Pz is a vector space of polynomials of highest degree 2 with standard operations and M2-2 is a vector space of matrices of size 2x2 with standard operations. a. T: P:» P2 T(ax? + bx + c) = a(x + 1)? + b(x + 1) +c b. T: P:» P: T(ax² + bx + c) = (a + 1)x² + (b + 1)x + (e + 1) c. T: Ma2 P2 T(: ) = ax + cx - 2
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