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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

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

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
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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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