Let T: R² P2 {where Pn denotes the vector space of polynomials with real coefficients that have degree n or less} be given by: T ([a²₂²]) = a₁ a₁x² + (a₁ - a₂)x — α₂ a2 Show that T is a linear transformation.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let T: R² P2 {where Pn denotes the vector space of polynomials
with real coefficients that have degree n or less} be given by:
T
([a²₂²]) = a₁
a₁x² + (a₁ - a₂)x — α₂
a2
Show that T is a linear transformation.
Transcribed Image Text:Let T: R² P2 {where Pn denotes the vector space of polynomials with real coefficients that have degree n or less} be given by: T ([a²₂²]) = a₁ a₁x² + (a₁ - a₂)x — α₂ a2 Show that T is a linear transformation.
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