Let T : P2 → P, be the linear transformation such thatT(1) = 4+ 2. + x²,T(x) = 3x, T(x²) = 1 + 2x + 4x?1. Is A diagonalizable? If so, find an invertible matrix P such thatP-1АР — D2. Find the eigenvalues and corresponding eigenspaces of T.

Given that: T(1) = 4 + 2x + x2T(x) = 3xT(x2) = 1 + 2x + 4x2 To find: Eigen value and eigen vector…

Answered: Let T : P2 → P2 be the linear…

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 : P2 → P2 be the linear transformation such that T(1) = 4+ 2x + x², T(x) = 3x, T(x²) = 1+2x + 4x? 1. Is A diagonalizable? If so, find an invertible matrix P such that P-'AP = D 2. Find the eigenvalues and corresponding eigenspaces of T.