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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: Prove that AAB = (AU B) - (An B),

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Q: 3.) Prove (cA)" = cCA) %3D

A: Let A be a m×n matrix so A=(aij)  1≤i≤m and 1≤j≤n ie A has m rows and n columns. By AT we mean…

Q: prove that 2. catX+c

A: We use that- sin2x + cos2x =1  so that 1-cos2x= sin2x

Q: 3. Prove that sinOtcos=1.

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Q: Suppose RC 1. prove that if B has a sup b, then A(U(B))

A: Given:- Suppose B⊂A and to be proved if B has a Sup b, then λ(ϑ(B))∩ϑ(B)=b

Q: 1. Identify which theorem will prove that ZEDC = ZDEC= ZECD if DE EC = CD. A,

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Q: Let feC-2,2], fo-o. Prove that Max -2

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Q: Prove that if |z| = 3, then %3D 5 2z – 1 7 - 13 4+ 22

A: The given is related to complex numbers. The solution is explained below.

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: b)Show that, 6(z, 3zy – y' and (z,y) = -+3ry are harmonie

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Q: of the suface the in tasechon of what is the fomed by y?+ z?=l and x?+z?=\

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Q: 1 Evaluate using Convolution theorem : L

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Q: - check the exi's tence of limol of the Lunetiom 41n at X= 1 %3D 2X+/ こ Xラ-3

A: To check: The existence of the limit of the function. Given: The function is fx=2x+1     -1≤x≤1x22-3…

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Q: 8. Chords AC and DE intersect at Point R in OQ. If AR = 6, RC = 7, and DR = 3, what is RE? %3D %3D

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Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

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Q: Arnold says that 25 = 3, and he uses the picture in Figure 3.30 to support his conclu- sion. What is…

A: Given that: According to Arnold reasoning:  223=45

Q: 2), Compute SE. di where Fュく-,) C is s shown

A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

Q: 1/3 If (x+iy) =a+ ib, Prove that

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Q: 2) of Ec, 4" is convngend can we conclude that coch of these are comvergent: (4)

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Q: ) Let z be a c complese number then cos ( 58+2) is bounded in C2

A: Since, sinz and cosz are unbounded on C. These are unbounded along horizontal axis .

Q: =8, d=9 ation u such that (a, b, c, d) = p

A: The value of a, b, c and d are given as follows, a=5, b=13,c=8,d=9. To find the permutation μ, such…

Q: Prove that Vtan a de – 7//2.

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Q: *10. Suppose AB = CD, AB 1 BC, and CD I BC. (a) Why must AC BD? (What congruence criterion…

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Q: Exercise.2 Prove that cos-1 z =- In(z ± Vz? – 1)

A: The given problem is to prove the given inverse complex trigonometric identity. cos-1(z)=1/j…

Q: If delta is large according to Cohen's classificantion, then the difference between u1 and u0 is…

A: Given that - If delta is large according to Cohen's classificantion, then the difference between u1…

Q: az Q.7 If z(x + y) = x2 + y?, show that lax = 4 ду. - +(1 - ax ду.

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Q: Suppose csc(4) = 2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII %3D

A: Given that                                     we have to find value of…

Q: A, Az, An are independert,2) PLiln)=r9)-1), where Bi is eitler Ai or Ai for izlityn in please proof…

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Q: Let Polynamial. has infinitely mny Toats, R-ZO7. Show t the (1,0)xin roots, Sol

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Q: If x<y, prove that x<(x+y)/2<y?

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Q: 7. Let B =- and = are bases for R? %3D

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Q: Fiven with z1 = (-3,1) and z2 = (1, 4). Show that |21 2| = |21||2|- %3D

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Q: v. Let Ac S, prove that P(Ā) = 1- P(A)

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Q: 3. Prove that: na” u[n] = az (a-z)2

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Q: 3. If u= (x+y +z') , prove that +y

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Q: Explain why the funclion (2)3D 12)=52-6+zcos Z-Ze is. entire ?

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Q: cos (o,+ O>)+ ì s:in (8,+Ə.)) Prove this kW- Mon 183O

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Q: Theorem 5 there is auniqe Reul for X=2 Sit X ER

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Q: Q1/ Prove that (Sa,0) is not Comm Sroup.

A: To prove the non commutativeness of the group

Q: Prove that (i) Res (tan z, r/2) = - 1

A: Here,we have to prove that Res(tanz,pi/2)=-1

Q: Compute Simits If they the eist 8+iz z²+4 hit Zマ-2 Re 2

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Q: Compute (2sin z -) ) da Show work but don't simplify.

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Q: If p,q,r are prime number but p is not equal to q, then what is gcd(p,q)? What is the smallest…

A: It is given that p and q are prime numbers. Assume that gcdp, q=d. Then, d is the greatest common…

Q: 2. Sketch 0 in standard position if cose = 8. and deter %3D

A: Given that: cosθ=-817

Q: In AJKL, JL is extended through point L to point M, MZLJK = (x + 9)°, mZJKL = (x - 2)°, and m/KLM =…

A: The exterior angle is equal to sum of two opposite interior angles. We will use this property to…

Q: 10- Prove that a.b3D la+bl2- la-bl? /4

A: Prove that a.b= la+bl²- la-bl²/4

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

A: Given :A≠∅A ⊆ B

Q: (b) Show that when dist(x, y) = dist(x, –y), then x and y are onal. orthog- %3D

A: Given  dist(x,y) = ||x-y||