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det TiP M,2 be defined by -Q,X + QX + agX ). Show that ī is a linear transforimation and find T Cax+5x²)

det TiP M,2 be defined by -Q,X + QX + agX ). Show that ī is a linear transforimation and find T Cax+5x²)

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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Let \( T: P_3 \rightarrow M_{22} \) be defined by \( T(a_0 + a_1 x + a_2 x^2 + a_3 x^3) = \begin{pmatrix} a_0 & a_1 \\ a_2 & a_3 \end{pmatrix} \). Show that \( T \) is a linear transformation and find \( T(2x + 5x^3) \).
Transcribed Image Text:Let \( T: P_3 \rightarrow M_{22} \) be defined by \( T(a_0 + a_1 x + a_2 x^2 + a_3 x^3) = \begin{pmatrix} a_0 & a_1 \\ a_2 & a_3 \end{pmatrix} \). Show that \( T \) is a linear transformation and find \( T(2x + 5x^3) \).
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