Question

PLEASE SOLVE IT WITH STEPS AND EXPLANATION

DEFINITION Set Addition If A and B are sets of vectors, then the set sum of A and B, denoted A+B, is A+B (R:-a+6 for some a A and beB). 17 {-} Let A B , and -span 17.1 Draw A, B, and A +B in the same picture. 172 Is A+ B the same as B+A? 173 Drawt+A Consider the line t, given in vector form by t Can , be described using only a span? 174 What about using a span and set addition? Span Span The span of a set of vectors V is the set of all linear combinations of vectors in V. That is span V=(: a,,+ a,,++a,, for some ,,..,eV and scalars a, a,...,a,) Additionally, we define span() -(0]. 15 Let , and iy 15.1 Draw span{,). 15 2 Draw span 15.3 Describe span(i,,2) 15 4 Describe span(,, ,). 15.5 Describe span(7, , ).

Answer 1

LU, o the A- 914]), 6=111, 12 lisbon ? +1). 1717 A+63 []+[.], [i]+[+]} =131.12] 000 AUD 10 (20) The blue veetas denotes A The bed veeter denotes B me black eaten denotes Atb A&B 12 Y 1+0= 17:]+[:], [:]• 4:1} 17. 13 BA ] 1 + ] 29131,1213

so A+B = B+A. - 17.37 . lz span {A} dena span { [+]}+{[2]} . Con lta in paralled to spon{11} A (1.01 7 lta 174) le= + f'] +[:] - rt+I! l -4+2 1 of possible let la: A SER so sx=tt sy = -4+2 Af A=0 fat and t=2 , contradiction. san so l can not be written as span of some reelen-

o Nao ". la= t[:] +fe] (1,2) bacalled to wla sbon +3} laz spor 17:33 1733) 16) ū = [!] Oz f+] Uz = [?] į spon quis low s por que? H i shenguss 2) afon gay?

- 15.37 Comiden ' 13-270 1. Hence qui es} basis of R2. Hence - spon que le} = TR2 15:47 Us = :1-27:] =2 te 1. Uz lies on sponsole} - so spon { t Iz} = spon quis. 15 4) + орох цаг, сарт 5%, 4, 4, S = spon qu, os, us] = TR2. [In the groaph a denote [] by (2,1)]