I just need help with c), d) and e) 2. (a) Show that the set B = (v1, V2, V3) defined by:10V₁[f]2 ==form a basis of R3(b) Consider a linear map f: R³ → R³ and suppose the matrix associated with f under thestandard basis of R3 is given by:1-1-112Find the image vectors f (v₁), f (v₂), f (√3)1*-()12-3 1-3 2-3 2 Define the vectors w₁ = f(v₁) and w₂= f(v2), where w₁, W₂ € Im(f). Show that the setW = (₁, ₂) forms a basis for the image of f.You may assume without proof that the image of the linear map Im(f) forms a subspaceof R³.(d) Define a linear map g: Im(f) → R³ given by:g (w₁) = v₁,g (W₂) = V₂Show that fogof=f(e) Based on your results, determine the validity of the following statement:"The linear map go f is the identity map."

Answered: Image /qna-images/answer/6a2166b6-d0ec-4bd9-a9e4-48febaaf7c44.jpg

(c) Define the vectors ₁ = f(v₁) and ₂ W = (₁, ₂) forms a basis for the image of f. = f(v₂), where w₁, 2 E Im(f). Show that the set You may assume without proof that the image of the linear map Im(f) forms a subspace of R³. d) Define a linear map g: Im(ƒ) → R³ given by: g (w₁) = V₁, g (W₂) = V₂ Show that fogof=f (e) Based on your results, determine the validity of the following statement: "The linear map go f is the identity map."

(c) Define the vectors ₁ = f(v₁) and ₂ W = (₁, ₂) forms a basis for the image of f. = f(v₂), where w₁, 2 E Im(f). Show that the set You may assume without proof that the image of the linear map Im(f) forms a subspace of R³. d) Define a linear map g: Im(ƒ) → R³ given by: g (w₁) = V₁, g (W₂) = V₂ Show that fogof=f (e) Based on your results, determine the validity of the following statement: "The linear map go f is the identity map."

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 30EQ

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