Question

Problem 2 (12 points, 6 for each part) (a) I'm thinking of two vectors ū and ū in R2 such that the standard unit vectors ē; can be expressed as ēj = i + 3ū and ēz = i + 50. Explain, preferably without computing my vectors ū and v, why they span R2. (b) Compute the ū and from part (a).

Answer 1

ū, v E IR² such that ē, = u +3ī & ez = 5 + 5T a Let (or, y) E IR EJ => [])+( = x et y ez = 2 (ū+3v) + y (a +53) xū+327+ yū + syv = TQ+y) ū +(30 + 5y) v 3 € spandu, u} - IR G span {o, o} But u, c ER span fu, hu, } 12 span {u, a} C IR? je Now to find u 4 Assume u = 50 q va Uz

따 = 3 0 2 V₂ : FU+3V U2t 3년 0 . u,+3V | U2t조별 그e 0 2) Now, = HT T) t5 0 ) Uz 는 - 이어 U+5V U2t5V2 CO u+ Sy- 0 3 U2+5= = | 4 u타5vs (-5v;) -5V, +3% == 2 -21 V U-5 = -5 (之) =

Page No. Date U2f3d () =) -3V+V= 킁 2V2= V는 :g = -3(% U2 를 u - ui 2 52 v= V) -) 늘