Show that if A is nonsingular and AB = O for an n × nmatrix B , then B = O .

Q: 1. Let U2 = 2. fui, 4.} is an orthonmal basa fo IR Show that

A: The set of vectors v1,v2,…,vn of a vector space V are said to be an orthonormal set of vectors if…

Q: 6. In AABC, ZB = 90° and BD I AC prove that BD' = AD.DC

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

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Q: 4/ur grans funthon y"-Uy't3y = et

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Q: E valugte the cube raot of z when 2=27 Cis(210) ( Let 0s GS360°) Smallost ☺ ualus) targonst ualue).

A: Since you have submitted two questions, we'll answer the first question. For the second question…

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

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Q: 12, GIVEN: JKI KT, ET 1 KT, KV TL, IL EV. PROVE: AJKL AETV. T.

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Q: det(A) Show that det(AB-') = %3D det(B)

A: Consider, Let A and B be the two n×n matrix, Now Consider, detAB-1 We know that the theorem, Let A…

Q: Use De moivres theorem to determine (3-4))"C4cis 30° )ieave your answer in 10 CiS the Formof Fciso

A: According to the given information it is required to determine the value of

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

A: We have to simplify

Q: A hransfoomation is definad by Hhe axa matox A=-a b-a atb Ifois an odd imtreger, prove %3D ushere a…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: is a conplex saries of nunbers and for VNEN monert an, bn ER Let 2n- an +ibn. Show that if Ź 2n =…

A: Given:  ∑n=1∞zn is a complex series of numbers and  ∀n∈ℕ, an , bn∈ℝ Let zn= an+i bn To show that :…

Q: Consider a robot arm as given in the following figure

A: answer is in next step

Q: Suppose thet the filowing Aransforuution Conneclss the (x') and (ti) codmate ک ماول se4ス?) e え(スーx)…

A: Handwriting solution given.

Q: 4) For A = ajax + azāy + azaz , B = b,ax + b2ay + bzaz, show that A.B cos 0 = A.AVB.B

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Q: 0/ the Valke of & that makes the Velteof the fumetion 2.

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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: If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

A: The given statement means the following.

Q: 5. Prove that if A and B are similar then dim(ker(A)) = dim(ker(B)).

A: We have to prove dim(ker(A)) = dim(ker(B)).

Q: .Use the De Moivre's Formula to show that if z = (cose + isine), then z" + ; ÷= 2cos (n8) and (금) 3…

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Q: (b) Compute r if: arctan r + arctan 1 = 2 ( arctan z arctan

A: tan-1x+tan-11=2tan-1x-tan-113

Q: if it was Mzn (R) was =a,br Prove that MzmC to

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Q: Complete a two-column proof. Given: ZRSU VST Prove: ZRSV LUST

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Q: In ARST (not shown), mZR 45° and mZS 64°. Find m ZT. %3D

A: Given that, In triangle RST, m∠R=45∘ and m∠S=64∘ To find:

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: Suppose, X0- Binom(m,0)and 0~ Beta(a, B), then E(X) is equals to, a) maß b) aß ma c) d) me

A: Given: Suppose,  Xθ~Binom(m,θ) and θ~Beta(α,β)

Q: Given: ZB ZD Prove:A ABC -A EDC в Ma com A D

A: Explained below...

Q: Show that every positive sol fron of Ay + B, k=osl,2- & bosunded, %3D JK is i-e, ogy sB-if A<1. 1-A

A: Given yk+1=Ayk+B, k=0,1,2,... Then the objective is to find the solution at which the sequence is…

Q: In AABC andAXYZ, AB = AC = XY, BC =Y Z and mZZ = 90. Prove: mZX > mZA %3D

A: We have given two triangles , ∆ABC,∆XYZ and AB=AC=XY and ∠Z=90∘ . and BC=YZ We have to prove that…

Q: 6. Show that (1) Cou(B1, g) = 0 (2) Cov(3o, B1) %3D

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Q: 3. Show that S, has the presentation (x, ylx* = y? (xy) %3D %3D

A: Given: Group S4 We need to show that S4 has representationx,y|x4=y2=xy3=1

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: SHOW that V Ź a? Jor a, E IR when His ineguaity e kold .

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Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

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Q: In AABC, AC > AB. The biscctor AD of ZBAC meets BC at D. Prove that Z ADC is obtuse. B C

A: In ∆ABC, AC&gt;AB. The bisector AD of ∠BAC meets BC at D.To prove that ∠ADC is obtuse.

Q: 3. 2. If A is 2x2 matri x aud Á = A, but %3D A+ A. show that A= 0

A: The solution is :

Q: Use the diagram to prove that ACAS ATAS. A T. Given: CS = ST and mzCAS mzTAS= 90 Prove: ACAS= ATAS

A: Given : CS ≅ STm∠CAS = m∠TAS = 90°

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: 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: 1. Prove with the usual notations that: (b) A + V =- (a) EV = VE = A (c) A= SEZ

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Qsit Prove that the Centre of a gp îs noymal. of

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Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: Given: AB = AC, RB = RC %3D Prove: SB = SC %3D B A- R

A: Given÷ AB=AC,RB=RC PROVE÷ SB=SC

Q: Find the angle between x and x4 in C[0,1] with its standard inner product.

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

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Q: Solve the following Linear Homo, y" – 4y" – 5y' = 0 - %3D

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Question 2: Show that the set S = {rVT + V2:rE Q) is dense in IR. Explain and show your work.

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Q: (a) Prove that x, y = -1, y = 1 1 (b) Prove tha and n: m and

A: This is a problem of Number Theory.

Q: Let A + 0 and ACB. Show that NB CNA.

A: Given :A≠∅A ⊆ B