MATH 218 Problems Solving Session, Spring 2007

Math 218 Solving Sesston( Set, Apa. 21 1007) nearer aab wrt ao and LL nw scala. [an b Standard Addition and scala Uh Qs cation see Eby eee a ee (at O49) 72 ya . (xan) ef ) (xrppabely) oye y! i lee) vty! ” | ‘ a w+ O, = w =f Xtc Lang) +(c+4) oy \ KAY be 4rd my Y There fove , O,= [< 2] . oOo oOo Aviom S: check that uz Hees) Geos) lety a) ute au a6 ney Key 3 hexiom 6: ke R ku=(kx k (ery) = ke fex+ eV bis ky Leealy 7] Acomt: aw scollons Note: If ve) [a sb] tee et ‘ : then Fr _enanrphe. axiem 6 doesnt wovl singe i a & V hue al ' F | kyy k 9 we should 1f or per in V then instead of "7 hawe R xy. 228 ex, Zo an if we take Tt Is not a Ve chr Space since 3 B= [o) 2] Bo aloo a 2x2 inwedhbbe mabrix Bt A+B= [3 2 not rer bbe SO Asiom | doesn’t hold : oon: (Note: Nobu thot aloo ftiam 4 deseon’t hold singe Q=[22]> not in the vechn space page 238 ex. 5 (2) We nym makues A suck thet AB=BA for a Fred nxn madrip B woo A | AB=BA § Te set af ob de a rbopace check © +f wwe eW Hr usveelW? and war in Win ul whi AB= BA, woh, whe A Be BA, “Thee Aine. (A+ AG = AB+AR. BA + BA = BCAtAY % wot So the nelubion Space ce dene ith , asamenc eguah'on yo tt P be 4+eR. j- Ht Zz 2a t pean 239 ex. 9 (a) R= = Atxa4x? Po = }—*%tPx™ Pye 342%+ 5%" Can -9-4x-15x%* be eqrol te Lip, * fet %& fe Be Somme be, be pk! -9-4x-150* = Lprkprkp, —t , (deat 4 k, (\- x+3 oe) k (34 2x50 ) = (thr hiv) + (b -k , ttk x 4 (uk, +3k 5 + 5k) x 2k +k 3k = -3 k - K+2k, = 7 Yb e3k+5k = 715 _ to o-1 2 \-* jo] t= 2 * ! 3 A217 15 1 3 \-3 E 3+ y 3 5 \-'s 4 3 5 I oF 3 -7 Io -) 2 |-F#57 sm -l & >= fit 3 3 | } 'c 23 {53 oo & ly eo o || 4 pege AYo ex, 23 (a) Folbe 44 b+ 0 So “yt K De pobakisn to The aydlim Ax=2b. Fo ket we gat usv EW fro alu eW for vrO wre a ku ew Fo aQ@d wEw . (a) Foe wath WOW, 0 solepnce of V Gven. Wo te a bape of V wank: jf re EW Mh hen us ee W Aly er scalar kue Ww AW, | (e) Fabre Counlirenanple Spon § CUNY 2 Span CU), Gr} Vole: af Wand Ware Anbanaces , WOW, reed not bo / fou exanphe, W b the =x Was the Line i Both ane dubspaces buk WUW, 4 pot . yok : | | > aa Her co a sebadt S’2hu;,-- of of . ¢ vithouk loss ob a non trivial 3 elton Cy WW =o Ss eee