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Unit-1 Detornunait & Function - 16 Mabks * Deters wnat Ay + by YaG QUtaM ed abel. ee SAG —\ ‘ al 3 Fe aT cE =! Fa £ a sc ¥ BK Deterrminout # Solution of 2X2 Deleymdnant 27 leeding element Sl ee tee ley seis? re dg Mba eee LE se Stdbsidiary Patncipal dy 2x 2 is onder of : C no rn A4encd =i Gq mie ee me til Detemwinart * aly detevmunant is always square type 9 AXQ 3 iy LCA. eta). * Solve the tollocwiney Det eywinends, Sr 2 -3 « Hapadrng 2 iis a 5 ie See a | * |q | 2) wae ohh 9 AG Sing — © la tend * Fs 2 Ce cine HEnee,. | SEEO L eH Ms oa <3 O then... a ae XL tilts BURL eect Mi ee * Tt A Py te ye Se IR le ches ike iad a aa | Scanned with CamScanner X% _. HE 6 a ‘= 0, thew. ae ee, Boal. 52, at |% an so then x= : * 2x2 PEs mane Myt+ 2-4 x. = a BE peg), (tS ae J— + — ay by | so) a re Y > order cf ee % be Gl 42 bg C2 Row Coluwwe * selution of 3x3 Detersminent (by Row & column anes method) abyss Ds aces a 2 2+ a4 vele ae ae bey, 3 = Oy Cha (a= Cy by) by (4203 - 93) + 4(A2b; - by 43) gL ae a yee Ce) 1, Pe abies ae | ga * m2 \3 4 9 \2©12) * D er a NE = it gynieade cod 2 78 3 Re $ dag BK) pe) | Mes fale) as) S 3 a4 it au SP =2 = 2 ey = Sade 4 fo) = (2B) ee ee abc (R,=R3) cae 2 cab C Scanned with CamScanner * Functioy * let A and B be te nen-emPty sets, rt eV ery clemet ot fp [Ss related to a umi'que olement of B thew the aelatien fs colled the Funchen t ; Co- Dome) | > y=fou ts the eelecHen for Independent Yartable cM eA and dependend varreble 162, x fi: AB Fix) = 44. find fe1) Ped) = 4th =o x f£:A>e feo) =c44 a -{4, 2,34 a> 123,406 | fay = 2 feo. £ (223 =a a ~ hu) > Sy fesy=§ “i * 44) =9 ay fe41y =f ca) Fury) = Fe) f(a) =2 => ee =i BE ae Scanned with CamScanner * “Types of Function * one-one fuctiog = ftoryy = fem) = Ny = 90 * Mary - one fucttan => gt fumetian os nat One one then t48 Called Mow -one furctt ar, SF 6dd functions = = fecy =— fen): (x) = x? fix) 2 pa = _~ x = —ttx) a3 js om odd function, X even funetton = fox = fen) 2 | fG0c9 2 9C ft) = cx = ct = fa) cA Ws amu eve Punchan, ~ Scanned with CamScanner . = A ilies * => fa)s bogx Hur prove dat (1) try r= fen ¢-Fey) WF 2) = Ftxr— Feu CH) Feed) = 2-fexy, f 3 RIL ftep seh then prove tc C-finy.ftyy fea ty) Ci) pe fens), * It ftxy=a™ the Preove ‘ee ty fta ty) = Ftan- Fey 9 OM) feo 47) = =—feod Fey), x It feo Snes Alias preonve Met fuct) — foxy =ca-19Ftx) * Tt foo = ig Hyuy preove thot Kota) Ft) = after), & It tty = Tix preve rect finy+ (4) - i ran * wt feof Hur chow Huot fen fO4)= & 1g Pep = ee OH PT tH fort FER) = © ev) foo — fee) = a. fen) Cth) Ftor- fen) = 4 x It foo = log (- ) Hen PT, AGO oe om hog (S45 # It fex) = hog (=) fhen #7. Fou + Fer) = Fees # tt Foo = beg (PE) ten PT fon + fom Be (oh Fix) = bey os Hua. PT. (22 ) =f. fey x It Fou = Leg avd gur= x then tind fq). x Feay= EE thun ‘PT x + (Foy) +4= 0 Scanned with CamScanner 4 * a er elw show aah atin) « ACF = = Fla) ot ye ses thea aS aes ot = = 00), iy Fig 4 Eee Scanned with CamScanner | a 4 1 ' } Vt ‘a mR Mla . aye ® boyd - boge toga. --. Jog 4000 > — nog 3 WY Q a . nee hog ™ ® bog P4 Miogy “e . ae * x tt heg 9¢ legax = legiv Es log eo | a Hw a2 * log a > x 1oq (x1) Hog CK n \ lo lo x Ie 5 dst). then Migs | —_ tie M4, bi: hey” | Ing 2 OS eee 4 ., It. + iis log, ee ft. % beg x toy? > — bog 54 » Leg Ceme) + heg Ccote)= —— ts + Jogat fog & as. + logat lege =— x beym — leqn= —— |oy 32 = log \6 = —— x logat = Jog gq > — x boy3r a bale =—— watt lege = 4 an Sa ye +t leg o'© dyur &= — Scanned with CamScanner dibs ah aes «ni re (45) +n 2 £4 log (22) * ba (2 )- leg Cig )tha(Z) * PT dng GAS) 2 20g (4 rh Vabaa Sue bloga PPT bog (x +-Jx%= 2) log (EDD =O. % PT beg (Wet +x) thoy (frat -2) =o pr hog (4) 44 log (SL) —tet Qt) log lo A BmpIAY Joga +4etoalts ) ra leg (5) +H ie 2 cas = of hcl aca cya (og,%4? Mok: ey Z * Pt og ‘sad «pt beg stg % +99, 75 ace ile? i lg ; A pt tog, Leg2. Joga = 4 akg am io leg 7 + Pt a a a8 bogs > Weg Fog, “Cee ah + iogah ae 7. ios, Toa 24 it % a qh “ © 2@ ae +] = i re L an, : ee ; \ ; abe [gy abc lo a _& ‘a te “a + aie ¢ an og oO dog Log ~ a4 ae Z eT. (64,0 194, 6 leas B 1 ++ fide a4 log tet dtd beg tta — - eee Scanned with CamScanner 
