Linear algebra: please solve all parts correctly and handwritten Problem 3 As a reminder, RN denotes the set of real sequences (uk)ken andS :RN(uk)KENRN(uk+1)KENi.e. S((uk)keN) is the sequence whose kth term is uk+1 (for example, S((uk)keN)o is u₁ orS((uk)keN)1 is u2....) Let4:RNRN(uk) kEN S((uk)kEN)-3(uk) KEN→i.e. ((uk)keN) is the sequence whose kth term is uk+1-3uk(1) Show that is a linear map.(2) Let (ak)k be the sequence, ak=3k for any kN. Show that (ak)k is in Ker().(3) Let (uk)ken be in Ker(). Show that uk = 3kuo.

Given mapping is that is (1) we have to prove that for this let then. .Thus we get for all this…

Problem 3 As a reminder, RN denotes the set of real sequences (uk)keN and S: RN -> (uk)KEN RN (Uk+1)kEN i.e. S((uk)keN) is the sequence whose kth term is uk+1 (for example, S((uk) kЄN)o is u₁ or S((uk)kEN)1 is u2....) Let RN 4: RN (uk)kENS((uk)kEN)-3(uk)kEN i.e. ((uk)ken) is the sequence whose kth term is uk+1-3uk- (1) Show that is a linear map. == (2) Let (ak) be the sequence, a = 3k for any k€ N. Show that (ak) is in Ker(). (3) Let (uk)ken be in Ker(). Show that uk = 3kuo.

Problem 3 As a reminder, RN denotes the set of real sequences (uk)keN and S: RN -> (uk)KEN RN (Uk+1)kEN i.e. S((uk)keN) is the sequence whose kth term is uk+1 (for example, S((uk) kЄN)o is u₁ or S((uk)kEN)1 is u2....) Let RN 4: RN (uk)kENS((uk)kEN)-3(uk)kEN i.e. ((uk)ken) is the sequence whose kth term is uk+1-3uk- (1) Show that is a linear map. == (2) Let (ak) be the sequence, a = 3k for any k€ N. Show that (ak) is in Ker(). (3) Let (uk)ken be in Ker(). Show that uk = 3kuo.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 92E

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