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 [8] for to be in Im(TA)? Is T¼ surjective (onto)? (4) Let us denote ū₁ = [½]. Find TÂ(ū₁). Is there any relation between T₁(ū₁) and ū₁? (5) Let us denote u₂ = ū₂? Find TA(2). Is there any relation between TA(2) and and and (6) Find TA([1]). Is there any relation between T₁( | (7) Find TA(). Is there any relation between TA( ?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 50E
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Linear algebra: please solve first 4 parts handwritten and correctly. Strictly handwritten plz

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 [8] for to be in Im(T₁)? Is T¼ surjective (onto)?
(4) Let us denote ū₁ = [½]. Find TÂ(ū₁). Is there any relation between T₁(ū₁) and
ū₁?
(5) Let us denote u₂ =
ū₂?
Find TA(2). Is there any relation between TA(2) and
(6) Find TA([1]). Is there any relation between T₁( |
(7) Find TA(). Is there any relation between TA(
0
and
and
?
Transcribed Image Text: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 [8] for to be in Im(T₁)? Is T¼ surjective (onto)? (4) Let us denote ū₁ = [½]. Find TÂ(ū₁). Is there any relation between T₁(ū₁) and ū₁? (5) Let us denote u₂ = ū₂? Find TA(2). Is there any relation between TA(2) and (6) Find TA([1]). Is there any relation between T₁( | (7) Find TA(). Is there any relation between TA( 0 and and ?
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