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Problem 1 Let A = (1) Find the domain and the codomain of TA- (2) Find Ker(TA). Is TA injective (one-to-one)? (3) Is there any restriction on a, b, c for [6] for to be in Im(TA)? Is T¼ surjective (onto)? (4) Let us denote u₁ = []. Find TA(₁). Is there any relation between TA(1) and ū₁? (5) Let us denote 2 = []. Find T₁(2). Is there any relation between Tâ(ū2) and ū₂? (6) Find TA( (7) Find TA( Is there any relation between TA( and ]). Is there any relation between TA([]) and ?

Problem 1 Let A = (1) Find the domain and the codomain of TA- (2) Find Ker(TA). Is TA injective (one-to-one)? (3) Is there any restriction on a, b, c for [6] for to be in Im(TA)? Is T¼ surjective (onto)? (4) Let us denote u₁ = []. Find TA(₁). Is there any relation between TA(1) and ū₁? (5) Let us denote 2 = []. Find T₁(2). Is there any relation between Tâ(ū2) and ū₂? (6) Find TA( (7) Find TA( Is there any relation between TA( and ]). Is there any relation between TA([]) and ?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 9AEXP
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Linear algebra: please solve last four parts handwritten and correctly. Strictly handwritten not typed work

Problem 1 Let A = 9-1-1 (1) Find the domain and the codomain of TA. (2) Find Ker(TA). Is TA injective (one-to-one)? (3) Is there any restriction on a, b, c for [8] for to be in Im(TA)? Is Tâ surjective (onto)? (4) Let us denote u₁ = [2]. Find TA(₁). Is there any relation between TA(1) and ū₁₂? (5) Let us denote ū₂ = [¦²]. Find Tâ(ū₂). Is there any relation between Tâ(ū2) and ū₂? (6) Find TA( Is there any relation between TA( (7) Find TA([]). Is there any relation between T^([ OOTCTO ) and ? 3 ) and ō ? 00T1IO
Transcribed Image Text:Problem 1 Let A = 9-1-1 (1) Find the domain and the codomain of TA. (2) Find Ker(TA). Is TA injective (one-to-one)? (3) Is there any restriction on a, b, c for [8] for to be in Im(TA)? Is Tâ surjective (onto)? (4) Let us denote u₁ = [2]. Find TA(₁). Is there any relation between TA(1) and ū₁₂? (5) Let us denote ū₂ = [¦²]. Find Tâ(ū₂). Is there any relation between Tâ(ū2) and ū₂? (6) Find TA( Is there any relation between TA( (7) Find TA([]). Is there any relation between T^([ OOTCTO ) and ? 3 ) and ō ? 00T1IO
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