Download Mathematics jee short notes and more Summaries Mathematics in PDF only on Docsity!
eS “Matz ices. DALES DY - =— ‘| Colin) a (Gs, om om ob oot = Chssangement \ = “ il —T Row, f 3 q ee Poe 1 St, Row 5 Ss A ay aad ots L ; Lake) Colmn = = _ es Algo bro. Sf od ni c8s, [ae BE for addition and Bubstoackon order should be came. [s 2S OFT toe Like Le a | Ly & J i oa { ae Sub tracton Pre | sae | —ar_| Seolot® Maltip ication. Bife 7 y [6..3.[ César koomultipGp faze) “IG ge ee) Sate 8S | = Distri bukve pre perty is —J eee) Nabd. a BYL = 2A s(A+a) = SA+ BRE 2] iy ee BS fae } Dalkiphoation, ae Rise auoNioam Ae cape = Onn Wath T ee | =e | 3xS a [24] (3 5] - [osu ws 403 7 2 fd | ty | Ey es ([_ Row Saas Pini MV doick. a a eee [Ue dind | loment No. =) Lino muitely Pow and Gul 24 O,, = 2 Rae AS Colum. Peopex tien 1 3° genvol , ABBA C997? $e ler GeO eee te ud ° BS G ® nero Need not whe A=ooF B=0 a) AB =Ac Need rot te bei h=c Gon Kee Rac) er SOE Ee: <9) Pes BA are ond B oss commutes |D pe = 268A" Bead B cen entcommute (Ss comma scve. wom i plicedion Bie clloge NEN madi 68 AS aie ordet) ee a ree me 2uso dont de - acBC) ef we lll UU QS Se — PAGE NO - te c 43 hero. CSaness oi) Son") iA = Sammealsic A Sked Symad = o T a \ = AtAT 4 A-AT \ i) D ® A+ BT = Symmetric pees <= Cys ik oS Sko2 Symmeterc pase ees || Gee gts | TeC Am )= Cot? ements Fo Squoae Pa, ‘eye 9 O23 athen. then odd ik) 5 E20 Gras | ae Adjorot _ oh, Mads x - fe Ad font = 2S = ayn O2 Oy Step 2 Sind mMepor- aun Or C23 Eee es View 8) Fa minor (Ae ony ( dekeradnosd. Toga O23 | Ae Mr M3 7 step 2 :- Cofachr. ci Ma M,, Myr Mes chonge Sign of, glements Ms: Mae [Res ot. Be on O&M tia, Mod Mey Mae Final Step tote teansfio e- +4 wes. DACKATA) = CodgA)A = IA] Eo Sao lp oS. ) adg CAs) (hag 8) Cody AD a) Jodj (a4 A) = = oe ee AD OW) adj ta, (aagA) = ‘Al Ba A eo sods Cui) [A capi SSN \Al non Singerias. wee pv to, eee a 2x2 4 a=fo b | + Bl d-b | ¥ [ea | eal =Y Susp diegonol are Sab q oh otg—b 2nd) o > Sigh change bd c 7 fox daadgsmoal Madux. | Bavesse of prelate, Lats Gasp ad! A* exist if A is : cae) ee a ) oS 7 lice Oo 4 Dryect heciprocal Sh oO o 2 ES) =e - 3 ie Ae j = _ Sime +sick Gy 3x3. # = + Nelle te) se || pi > Z a 2 -- 3 a ae ee at Ci os UW 3| RT A |e C/o Eo eer | cere m5 ql ae 2 2 =4L wt G Cancel +his then Cress mudi pty. mudttet hovizont corte png vUerticad. fy o J SuGe RECN) AS) = A @ AA fa BN Seo Regia? @ KA -1 pt is ; [3 7 — tila be { te KB ke a wae = dé «a4 & ‘gh 4 | | h j @® | VeAv =e lal whee n is order of A. _® Nolo ef, _ =i odd omer @ | eae ua MOS. 4 a" PAGE NO / » sare —~— the. Valin. _ 9 delce mie asl temas Sarns ao poy SJ - Sermemtet i AvanS hozmnabon 7 RR AHP ws CFG reels. (ATipe crenk | + —— f two 4485 L eas SF Rules ay =. + OR MR, Os pHreee. t ~ Al one J 4 au aay 4. ——T~~ oa — — SSS 4 ~ | Specie) determinants %” sap Me! 2 oe a> a be = Cx-wcy -2)¢e-x) t+ 2 1 z » yy? = (RY) Cy2) Z-X)Cxry42) SS eee ——_—_——— bc bc a | = ceed’ - sabe), By bb Wo) tfeYal ge ara} ee Rule etermenant ) mc CTordan method ) ey Reomogencus + Constant teem = zeae 2 | Tees ond Tips, 2) | Consistent + Solution exist Cunaua and sofinite) DUESatonsten + co Ssution 3 wy Taivied solution . aso, Cieey 25 + | ome sonoug Equaton ° == = - D=6 ake) = TRnike Bolotion = Taiaial = Non Anwe) a Uns a. Consistent - > ~ ‘ © Ladeahic, Ee vedio om PAGE NO.: ¢ = DATE: / u 5 SS ——— -| | Yr on® +bx +020 Cato) ~| fs a — - les =e Cee) =| r a a ~ ren =! * | Retation bekseen Roots and Goel ficients ~ | bs | i@) REM [5 iy IB <= ef a co H Qdentitien Vy XK +BY = Cat e)h-2<8 | aed id ot apt o> Gee ptyt ~ Bert BE ! As wi) 084 B= Cone - ane care? ww (8-87 = Corey - UKB ® foametion ot, Quadratic Fauation 13 &,p = Poots | xt ~ Csum)x + Product) <0 Neoton's Metned, £Powes of, Root) : obey + bb set —% Soin * ee I eh Bp OSoutobsh-, 4Conk= Oo | Ce vols) me 20 => then Sdentidy . PAGE NO.: § S donate: 7 1S ——— — : eo (> =- S50) Se ® n Fae ea aos - Ve : | ay j b= @® Has xe ewe Z fey \ peyaE ney =! S| BE Quadaatic Eg pation [ a ; a ~ ES less Sgmmebric anh + bo?+cx> 4+bx +0 =0 m9 og oited Bame Methed +@ z* se adaide. apart \ # bed) 40 <0 See} ae. alf aot \b-2\ + Bixee | te =o x) ] ea aH Es Condition Ses tom mo® scot, ——<—<——<——— = SS —=_ a ec alee he eS es ae Eva & Ai | Onx bux +0, =6 Ce Se | both soot Common | Ds Orly oe. yeot Commo%y ant een ‘ibe ee = Za = Sodtshy Soot Common) ee 4h.% 4er1=0 7H = Modiehy MH 24" with ay | a and a,ee? witha, F thik 4¢,)2 © = gobtact i rey) a) __- *C vse product of xoxt ! = jaa Sena ax \o eon Roots Ss 2) * ™~, Step 2 megk al) possiblitig iy sod. — Whe jwel wets We boteoeey 3 and S. — ors | aa | ~ A eee (ae Re a ti 4 ' a re { age ’ Step 2 = MD OFDH of ® -&/, © Gs) ” (>, Feod MBA Lo 29) z (ae Se eS Se eee — sk ails L leet chin ck | Ree j eI ey ns eee = ay a a . P A+6 = -b mE = C. i ( ey Ov hae 1 me) J Bees Sra ’ x © ao +b disc ll ai a Oo a a ie se x MasteR) se my adn Fe pte: + Ya " Wee mr bp HORN ee ae i. = ' yey Da ae SE —m-) . i Ab hy a Be) 4 1 eee ; || a Com eleme in — “TRG NoMETeY,” i Sdeotini SSG 4ee SB = 4 qu = Ot i Sed a O82 Bee%@ 2 taste = 2 pep } — coset 2 i) Cogecte - mt eo = t. re | : HORUS laa A Cae h Sie cr Eis Fane ton | | iE hae ay | = BOs a oe a ORE AM que) 7% No chang = - Sa en T oe, D4 ‘past Wi i Eo oa Uh (ae eventn) eg, SO a 08 bba IGA Ben Ste oe (aed : (GES) ean ae tly if \ Ce he = St lotsA = | a \E.ohitn has a = i ae =A ; : i Be es 2 SORces® +) CasAsin® _ 7s! Cog pda ‘5, ca-8 + sina cosB ~ cosAsin® | and Subtsac} \ : Cos CAB) |: Coen CosBo ~ Seah SinB , T ten cA-8) I: Cogh @SB + Sink SinB | a a — T > tan A +4ané . woe stenB 4 a 4ten Aten 1+ Aanhton& | Callao ee Cot p. Cabby. Lok A Cot B-i Lis] —) — eth - Bache 7 el “tee [ ete \ GTA Cot 4 Adel enol Sah cin HA) SINA-O) = Sta = SiO ces CAH) CoscA:8) = cot A > sir : FO CMt RHC) = tanh ++4an4 +anc ~ tandten®tenc | —— D- tanptanb —tanbtenc -tonc tone ny oe ® 2sinn 8G = SIocAt B®) +ainCA-B) ] tt (Se) a2cesA sin® = S9CAiB)-stoca-8) | (e) 2Cog A Cosh. = CostAte) +Co3 CA-8) \ Muti pli \ a @ sa2cinpsin& = cescA- 8) -Cosc Ath) i Nad ® | anc +500 = 2sinC+o) cos(c-9 sf =] i is Phe ( + Ad ol CS Te @)| sin -SinO = 2 ces (ere) sinCe-9) ly Pyltiphcotion t 2 2 t = : @)| cose ces5 = 200 Clr) ws C0) ' deidse bene ; 2 F oe. nl : @)_|_ cose =iCas Dac 283m C+0) incero) | | v es oo ; | | Sina6 = Jlo-2s5 Qypee =
Ondy in Cos —_ Fal Onky 2 doubfs og) ss 7; > A ramallet angie a ® Eee + Bacere) a Sin Gelaedie 8b sin CX #jEn-2) B)) \ ’ u a> | |isin DP, ( sim Ce + cn-a0 6 ) ¥ Vie x na G) | Cosa + tos Crt) + SaB Corte) o> + @S G+ n-2) P) | wo sin Piaf. costa tr-2) 8 \ | sin Bfo PA / ] 4 A fFKR 2- ange fn Ar 7 x - Fist tom Csmattest) ~ Summation ve B> cod Common diff) — Fim los - 7 on NO Of foemns | 4 QuATTON. on il hh a 2 — E PAGE NO.: Poste: 1 7 \ __ = iiiitiiP_,_,,_,_. SSS! _ | : Steptir Sint 22 ( Votiablo | hilo = ©% Med ago) = Sepia neni ®|@®. (igure out — Be 6 ae | < 5 encdaut) ©. Tjond 1 Stee 3) wi yet | 0 fees et oe i wth | an 6 si SiR ie Bede ke | ] ae SGenzol olution :- 7) Sao =sinx = O = nnt(-1)"* CPR) Cos & = Cosx + O= ern tn (ith) ten = tent = O= nm+% _ fy) Sin2@ =Sinrh W Cos? © = Cos? K OQ = mime vip tontQ = tent a og Sia ce es = 8 Step t= Find paincipa) Solution Step 2 DBNX= Sin Use veap 1 Sar /2 fosmula. Y Use SrewteHt for Gemal Qo/.. tos.