simple answers with explanations for three parts would do well. Thank you very much 4) Consider the following three vector spaces with corresponding basis:V₁ =R³B₁ = {e₁,e2, e3}B₂ = {1, t, t²}V₂ =R[t]<21V3 = M2x2 (R)B3 =- - ( ) ( ) ( ) ( )0Now consider the following two linear transformations:T (1)T(b)=a+b-ct + at²CS(a + a₁ + a₂t²) =00 - 02 01ao + a₁a2(a) Compute [T]²B₁(b) Compute [S]2(c) Compute [ST] and verify that [ST]B³ = [S]B³₂[T]B³²

Answered: Image /qna-images/answer/b6023aaf-39ef-49b9-9bff-6b41c5745026.jpg

4) Consider the following three vector spaces with corresponding basis: V₁ =R³ B₁ = {e₁,e2, e3} B₂ = {1, t, t²} V₂ =R[t]<2 1 V3 = M2x2 (R) B3 = - - ( ) ( ) ( ) ( ) 0 1 Now consider the following two linear transformations: T (₁) T(b)=a+b-ct + at² C S(a + a₁ + a₂t²) = ao-a₂ a1 ao + a₁ a2 (a) Compute [T] (b) Compute [S] (c) Compute [ST] and verify that [ST]B³ = [S]B³₂[T]B³²

4) Consider the following three vector spaces with corresponding basis: V₁ =R³ B₁ = {e₁,e2, e3} B₂ = {1, t, t²} V₂ =R[t]<2 1 V3 = M2x2 (R) B3 = - - ( ) ( ) ( ) ( ) 0 1 Now consider the following two linear transformations: T (₁) T(b)=a+b-ct + at² C S(a + a₁ + a₂t²) = ao-a₂ a1 ao + a₁ a2 (a) Compute [T] (b) Compute [S] (c) Compute [ST] and verify that [ST]B³ = [S]B³₂[T]B³²

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 16RQ

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