Plz complete solution with 100% accuracy I vill upvote it is my last post plz complete it. (a) Choose all correct statements:Let S be a linearly independent subset of a vector space R4. If the vector v is in R4, and it is not in S, then the setSU{v} must be linearly independent.Let W be a vector space of dimension 4. A spanning set for W must contain at least 4 vectors.The map F: M33 M33 defined by F(A) = AB + BA³(b) Let T: M22 → R2 be the linear map defined byT(X) = X(where M22 is the set of 2 x 2 real matrices.bsin (a)(i) Suppose that A is the matrix of the transformation T: M22 R2 with respect to the standard bases,S₁ =for the domain and= {( ) ( ) ( ) (9)}{6).()}*S₂ =for the codomain.Find the matrix A and enter your answer, using equation editor, in the box below.Әəxab sin (a)f∞ a Ωand B = {u₁, u₂} for the codomain, where ₁ =Əfəx(2) + X² (₁)where B =a 52(ii) Your friend Benedict is interested in the matrix M of T with respect to the bases S₁ for the domain(²)·(¹).Help Benedict by finding the matrix M and giving your answer, using equation editor, in the box below.and U₂ =EG5 5 12523 1 1, is a linear map.G

Answered: Image /qna-images/answer/6b78687a-0cae-4df8-a073-6cb098108b9f.jpg

(a) Choose all correct statements: Let S be a linearly independent subset of a vector space R4. If the vector v is in R4, and it is not in S, then the set SU {v} must be linearly independent. Let W be a vector space of dimension 4. A spanning set for W must contain at least 4 vectors. The map F: M33 → M33 defined by F(A) = AB + BA³ , where B = (b) Let T: M22 → R² be the linear map defined by T(X) = X() + X² (₂). where M22 is the set of 2 x 2 real matrices. 551 512) 3 1 1/ 252 , is a linear map. for the domain and (i) Suppose that A is the matrix of the transformation T: M22 → R2 with respect to the standard bases, S₁ = {( ) ( ) ( ) ( )} - {6)·()} S₂ = for the codomain. Find the matrix A and enter your answer, using equation editor, in the box below.

(a) Choose all correct statements: Let S be a linearly independent subset of a vector space R4. If the vector v is in R4, and it is not in S, then the set SU {v} must be linearly independent. Let W be a vector space of dimension 4. A spanning set for W must contain at least 4 vectors. The map F: M33 → M33 defined by F(A) = AB + BA³ , where B = (b) Let T: M22 → R² be the linear map defined by T(X) = X() + X² (₂). where M22 is the set of 2 x 2 real matrices. 551 512) 3 1 1/ 252 , is a linear map. for the domain and (i) Suppose that A is the matrix of the transformation T: M22 → R2 with respect to the standard bases, S₁ = {( ) ( ) ( ) ( )} - {6)·()} S₂ = for the codomain. Find the matrix A and enter your answer, using equation editor, in the box below.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 24EQ

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