Ti Ik'→ IR? be a linear transtormation 3). let defined by -E: Co all ER T C3 x2 + Show that T is onto but not one to one,

Q: Let z= y- 4a, a u'v and y-v- 3u. Compute On kum)-(1,1) -

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Q: Let G = Z31, S = {1,5, 6, 25, 26, 30}. %3D %3D Prove that Cay(G, S') is normal.

A: It is given that

Q: Let {u, v} be an orthonormal set in R" and let y = v13 u + 6v. Then, y|| is

A: Here, given that u,v are orthonormal. That is: u·u=1, v·v=1, u·v=v·u=0

Q: (b) En=1 m

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Q: Compute the orthaganal piojectian of ? onto the lina L through -6 and the origin

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Q: Suppose the conjugate z is equal to the reciprocal 1/ z. What are all possible z's?

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Q: 5. Prove that the baker map 2x B(z) = 2z - 1 <z<1 is chaotic on (0,1).

A: Given the baker map, Bx=2x,0≤x≤122x-1,12≤x≤1

Q: Let E={(r,0,z) : os es T, OS zs 1, 5Vzs rs 5. Compute

A: Introduction: The triple integral ∫∫∫Ef(x,y,z)dV with the region E=(x,y,z):a≤x≤b, c≤y≤d, e≤z≤f can…

Q: a) Show that fi (x) = cos x, f2(x) = cos 2x are orthogonal on [-7, n].

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: 7. i) Show that Q(2'4,i)/Q is a Galois extension.

A: The given function is, E=ℚ214,ii,e, E=ℚ24,i The minimal polynomial of 24 is  x=24Taking power 4 both…

Q: { (0,3), (0,1) is linearly independent in R? ylgn O Ins

A: The given vectors are  (0, 3) and (0, 1) To find whether they are linearly dependent or not

Q: alue of the pur C: |z| = (:-1)(z-

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Q: Let X, and X, independence r.v. have same moment generating function (1-) where isa, let Y=aX₁…

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Q: Find the fowien senies fon | X), -T<X <A

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Q: (4b) Is Tâ onto? How do we know?

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Q: Functional theory and functional analysis

A: According to the given information it is required to prove that:

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: Exercise 4 Show that for cach k EN it holds that kn-k < n! S n", Vn E N, n2 k. Deduce from this that…

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Q: a) Show that fi (x) = x, f2(x) = cos 2x are orthogonal on

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Q: if JERLA.b] and it hex)- J(x). except for finite mumber of Paint in Cab] then that he Rlab] prove.…

A: if g ∈R[a,b] and if h(x) = g(x) except for a finite number of points in [a,b] then prove that h…

Q: Prove that T2 is chaotic on 1.

A: Given that T2=2x0&lt;x&lt;122(1-x)12&lt;x&lt;1 The maximum for T is 1 at x=0.5. The dynamics of T2…

Q: If the i, j entry of A is i times j, show that det A = 0. (Exception when A = [ 1 ] .)

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Q: The orthogonal projection of y onto u is the same as the orthogonal projection of y onto cu whenever…

A: solution

Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

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Q: Let E Os 0s n, 0s zs 1, 8Vzs rS 8. Compute

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

A: We have given  matrix A is non singular and AB=0 for an n×n matrix  B. We have to prove that B=O

Q: Prove that F(z) = 81 8z + 1 is chaotic on (-1,1).

A: To prove: Fx=8x4-8x2+1 is chaotic on -1,1. First plot graph of given function with -1,1 as follows:

Q: @ Let A -a Find Cenditiens on a,b.c and d that AX =o has infailely many Solution. what must there…

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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: 2. Let S,T C R" with S being a proper subset of T. If span(S) = span(T), then T is linearly…

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Q: Show that Z, dv=2010 %3D if B= 2) : -1 Śn s3, ISySY,e

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Q: # if Alu) is a differentimble veetoru u and l A(W) Il = 1 . fonetion of Prove that dA is…

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Q: 2. Use Wronskian to show that fi = x, f2 - Inz, and fa C (R). z Inz are linearly independent in

A: First we will calculate the wronskian of given functions f_1,f_2,f_3

Q: Which of the following DEs are first order linear DEs?

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Q: Give en exem ple of e: neer trensforme tion thet is not invertibl. V-> v onto but

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Q: Consider Uu=4uzzy u(x,0) = u(x), u₁(x,0) = u₁(x), on the domain -∞<x<∞, 0≤t<∞o. Suppose that both…

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Q: 2 Given u -1 and U , for which w is the set {u, v, w} linearly independent?

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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: = 1, prove that 1. If a + u bě+ u Ć +U %3D ди ду du ди du - 2| х +y Əz

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Q: and are 2 soihions and w Cy,,Y2)(to)to what con conclude ? we

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Q: Let an 1+1/V2+1/V3+...+1//n , Prove {an} is unbounded. %3D

A: Given that, an=1+12+13+...+1n

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

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Q: Assume that a1, a2, ..., an E R (with n > 2) such that a1+a2++an = 1. Prove that af+az++a > 1 (Use…

A: Cauchy-Swartz Lemma : For any real numbers  and  the following inequality holds  ,

Q: 5. If u = ee Cos(alogr) prove that a'u 1(ôu 1 a'u = 0 + r ôr

A: Derivative.

Q: let FC k be a Galois extension with Gal

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Q: 2) Suppose S,T E L(V) are such that ST = TS. Prove that null S is invariant under T.

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Q: Show that if E,=1 a, diverges, then En=1 | |a,| diverges. %3D

A: Given, We want to prove that

Q: Let T be. a linear trans formadion

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