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2. Let T: P2- P2 be defined by T(a+ bx + c?) = a - 2b+ (2b – 4c)x+3ca². Find a basis C for P2 such that [T]c is a diagonal matrix. %3D

2. Let T: P2- P2 be defined by T(a+ bx + c?) = a - 2b+ (2b – 4c)x+3ca². Find a basis C for P2 such that [T]c is a diagonal matrix. %3D

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. Let T : P2 -→ P2 be defined by T(a+ bx + cx²) = a – 26 + (2b – 4c)x +3ca2. Find a basis C for P2 such that [T]c is a diagonal matrix.
Transcribed Image Text:2. Let T : P2 -→ P2 be defined by T(a+ bx + cx²) = a – 26 + (2b – 4c)x +3ca2. Find a basis C for P2 such that [T]c is a diagonal matrix.
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