3: Consider the linear map T: R³ → P2 given byaT(6) = (a – 2b) + (3a + 4b)x + (–3a + 6b)x².a) Find the matrix of T using standard basis for R3 and basisB = {x²,x + x?, 1+x + x?} for P2.b) Find dim kerT and dim RangeT.

Let us consider the linear transformation, T: V→W Kernel of T is obtained as Ker(T)=v∈V|T(v)=0.…

Answered: 3: Consider the linear map T:R³ → P2…

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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3: Consider the linear map T:R³ → P2 given by a T( ) = (a – 26) + (3a + 46)x + (-3a + 6b)x². a) Find the matrix of T using standard basis for R3 and basis B = {r², x + x²,1+x+ x²} for P2. b) Find dim kerT and dim RangeT.