2. Let T : P2 –→ P2 be defined by T(a + bx + cx²) = a – 26 + (2b – 4c)x + 3 cx?. Find a basis C for P2 such that [T]c_is a diagonal matrix.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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2. Let T : P2 – P2 be defined by T(a + bx + cx²) = a – 2b + (2b – 4c)x + 3 cx?.
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 – 2b + (2b – 4c)x + 3 cx?. Find a basis C for P2 such that [T]c is a diagonal matrix.
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