Exercise 1: Derive [2} rm (1]. {That is. express deltas explicitly] Exercise 2: Using scrne ccmputer prcgram that can perfcrm matrix manipulaticn find the pcsiticn cf a GPS device with the fcllcwing data: Pcsiticn of Satellite S]: (lfl, 12, 12) , distance to Satellite S1 = 1? Pcsiticn cf Satellite 5:: (S, l4, l4) , distance tn Satellite S: = 1d Pcsiticn cf Satellite S3: (T, 16, -S} . distance tc Satellite 53 = 1? Pcsiticn cf Satellite S4: (11, 14,?) , distance tc Satellite S4 = 14 Prcblemipuexle 3: (11] After expanding the squares cf Equaticn 1. vcn can consider the differences cf these equaticns: (i) + (if). (ii) (iii), and [iii] (i). and still get Equaticn 2 {with different 53) which would give the scluticn fcr (x, v, x) with cnljlr three satellites visible. [l1] Sclve Prchlem 2 with data fcr three satellites (chcse vcur favcrite). [cl But there is scrnething wrcng here... Shculdn't vcu get twc scluticns (why? Ccnsider the gecmenjr cf the situaticn). 1|What has happened tc the cther expected scluticn? [I-Iint: ch manv satellites wculd vcn advise in a twc- dimensicnal space? Draw the simaticn fcr twc and for three satellites]. [d] lEither interesting cr bcthering questicns? PrchlI- 4 (for fun}: Interpret the deltas cf Eq. 2 in geometric terms. Can vcn ncw reinterpret Eq. 2 and 3 in gecniettic terms