is a conplex saries of nunbers and for VNEN monert an, bn ER Let 2n- an +ibn. Show that if Ź 2n = 1+2 00 then E an =4 and S bn=2. n=1

Q: KLM is a kite. If mZJKN = 28° and mZKLM = 103°, find mZ JML. * %3D %3D K J M

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Q: 3, Given: mABD=m2CBD 4. Given: UM mZBDA= m ZBDC ME = RO Prove: AB = CB Prove: m ZM =mZR %3D %3D R M-…

A: 3) Here, the given triangles are ABD and CBD. Given that m∠ABD=m∠CBDm∠BDA=m∠BDC

Q: We defined NCE) = ZE for ZE Z Ii]. Prove N (Zw) = NLZ) Ncw) for all Z,W E Z6] .

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Q: 3) Let PIASR ond Thi AxC ßeD. Then his a Anction. Te Ø # 4 B and ø 7b cD then that h'(Y x Y% ]=…

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Q: Hor what salue of e dois th. a tollowng matrex haue an Tnverse Q. 2. 2.

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Q: Consid‎er a la‎mina t‎hat is in the fir‎st quad‎rant, ins‎ide the ci‎rcle whos‎e equ‎ation is x2 +…

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Q: evaluate the in! integ ral if u = 16+ ex then e* V T6tex dx = ( Jü cu=(ile %3D

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Q: Prove: Given that ll Xllo sl1x|1, <vñ lIXloo for XEL". 2 Show that for

A: The matrix p- norm = operator norm                            ||A||p = Maxx≠0 || Ax||p||x||p…

Q: A liner tragfematin defimeed by a malrıx let IRR be a lineor tras ler malin. defneed by Tv) - Av ;…

A: I have proved Linear transformation using the definition

Q: Given the mife has betweeu so oud $ 50,000 of msurauce what ios s the ebatily probabii tū between 0…

A: The conditional probability formula is, PA|B=PA∩BPB The row totals and column totals are,   0 -…

Q: Given z = 3 cis 120°, find z3 using De Moivre's Theorem.

A: We have to simplify

Q: 2. Given: XW XY, HA I WY, KB 1 WY Prove: AHWA ~ AKYB. K Y.

A: Given data is : XW¯≅XY¯ Therefore ,  ∠XWY≅∠XYW∠XWY≅∠HWA∠XYW≅∠KYBTherefore,∠HWA≅∠KYB     .....1…

Q: Given that n ≥ 2 , x ∈ Rn  Prove that there exists a y ∈ Rn in where y ≠ 0, and xy = 0

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Q: OVESTON Prove that A is inveitine if at0 and at b l Gind The pivos 9 A %3D a a

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Q: (- For all asb,C EZ,prove the folloNing (i)ala,1la, andal0; (ii)0la if and only if a=0; (iit)alb ond…

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Q: Hiw Prove that c=z²,'s coutinuous at z=z. O prove that: if Z#Z0 is dis continnity at Z=Zo, where 2o

A: (1) Calculate the RHL and LHL for the function f(z).…

Q: 3. Suppose AB=RS and mzB = mzS. What other information is needed to prove that AABC = ARST by SAS?…

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Q: 1. If r = xi + yj + zk and r = |r|, show that (i) div 0, %3D (ii) div (grad ") = n (n + 1) r" - 2…

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Q: Q, : which of the following are inner product on V,CR) where u=(81,Nz183) ,V=(BiB2.P3) 1) りとuvン=…

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Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

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Q: Prove that (aA + bB)t = aAt + bB t  for any A, B belongs to Mm× n(F) and any a, b belongs to F.

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Q: 2) Given: ZRAL E LYAL, ZRLA LYLA A Prove: AR = AY R.

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Q: if x, y>o such that x Sy then Vã svy Prove by direct method

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Q: The joint propabiiy fnelion sTrtwo disen Ete iandom veritbles ☆ and y is given bi flkr)= c(2K Hy)…

A: The given joint probability function is as follows:

Q: Showw Fom yex)=D90Y,(x) + a, y,(x) that seris sol utron is of the hene y,cx) contains only even…

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Q: (a) Let r = ri+ yj + zk and let r = ||r||. Prove that - (1) a

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Q: 2. Given: XW = XY, HA I WY, KB 1 WY Prove: AHWA~AKYB. W.

A: Given that XW¯=XY¯ in ∆XWY. So, ∠XWY≅∠XYWor, ∠HWA≅∠KYBGiven that HA¯⊥WY¯, KB¯⊥WY¯So, ∠HAW≅∠KBY=90°

Q: Let X be a random vuniable with PAF FlnS= %3D otherwise s Find the constunt c J Find ECH and Vor (xS

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Q: N is the centroid of triangle HIJ. If KN=9, IM=15 and LN=5. Find KJ K. N/

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Q: Write a two column proof. X B 45. Given: WX 1 XY; 21 is comp. to 23. Prove: 22 = 23 W Z Y 46. Given:…

A: As per our honor code, we are authorized to answer only one question at a moment. As you have not…

Q: omplete his praol of Theoren 1. B Cive ZA and ZB with AĎ || BẺ; AČ || BĚ. F D Prove: ZA is…

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Q: 19. Given: OABCD; BE | MD: M is the midpoint of AB. Prove: DE = BC %3D E D. A M В

A: We have the given figure as, Here, □ABCD is a parallelogram and in figure BE∥MD. M is the mid point…

Q: (a) Let r(t) = ti+tej+fk. Find ((1),4 × (?),1) - (1)a tuj

A: First we find out first derivative of r(t) with respect to 't' then find out 2nd derivative and then…

Q: a. Show that T: 1² → 1² defined by Tx = y = (n), n, = r, is compact where x = (5,) and where0 <r< 1.

A: Show that T: l2→l2 defined by Tx=y=ηj, ηj=rjξj is compact where x=ξj and 0&lt;r&lt;1. Definition:…

Q: Use Green's Theorem to evaluate >[2²y² dz + (yz²³ + y²) dy where Cis shown below. 90 O-384 O-48…

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Q: prove that tr(aA+bB)=atr(A)+btr(B)for any A,B belongs to Mmxn(F)

A: Let A=aij and traceA=trA=∑i=1maii.. Note that, aA+bB=aaij+bbij. Then,…

Q: -H.. OProve that fcz) =z²,s coutinuous at z=z, O prove that: if Z#20 is dis continnity at Z=Zo,…

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Q: Ex: © Suppise that the fuowing trausfruntiun Cowneciğa the (I') and (xi) coarduate رک سهاور؟ てス4ス)…

A: Given  x¯1=ex1+x2x¯2=ex1-x2 Required Jacobian is…

Q: Let S-(xeZ vmod12-8) and T (xe2| 4x). Prove that SCT but TgS La s-(rez| 3reZz, x-12r+7) and T-(xeZ|…

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Q: Let X, , X>, . X, be a vandam of size I For o hormol distribuien with unrur M and $6. IS 5 Xi = 132…

A: Provided information is ;  sample size(n) = 11 ∑i=1nxi  = 132 ∑i=1n(xi-x¯)2 =99 confidence interval…

Q: Let 1 an(r) : u(reie)e ino de %3D Prove that:

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Q: ZVYW E ZTXZ, WX YZ, and ZZ ZW. Complete the proof that AVWY ATZX. W

A: Given: ∠VYW≅∠TXZ , ∠Z≅∠W Also, WX≅YZ   1 Adding XY to both sides of (1). We can do this using…

Q: qu2 .01 ai anoitoni lo oonoupse a od (A oels bnnI.031 moitonl s of 1. Let m*(A) = 0. Prove that for…

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Q: b) Show that the following wo matricegane orthogonal tker A =-V3 -2VTO 3/T15 15 E/NTS

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Q: Then show that N(A) = R(AT)+ and N(AT) = R(A)+. %3D 11-1 02-3 -1 1-2 N(A) = N(AT) =

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Q: Given: ZYLF = ZFRY, RFY AFY Prove: AFRY= AFLY Y L State ment Reason 1. ZYLF 4FRY 2. ZRFY = AFY 3. FY…

A: We have to find reasons

Q: a- if w = f(u, v), u = x + y, v = x-y Prove that = ( - )* aw aw %3D ду du.

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