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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.

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.

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