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

Q: Let w = xydx + 2xdy - ydz E 2'(R) and let a: R a(u, v) = (uv, u², 3u + v). Compute do, a*o, d(a*o),…

A: Given ω=xy dx+ 2x dy - y dz in Ω1ℝ3x,y,z And let α:ℝu,v2→ℝx,y,z3 be given by  αu,v=uv, u2, 3u+v. To…

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 X (2,3. 4) and de fined metrie on X as d(x, y) = |-y Find open ball B (2.2) = (0) O (2) 0 2.0…

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Q: Let fxy (x, y) = 6 (x – y) , 0 < y < x < 1. If E (X) = , E (Y) = Cov (X, Y) = then %3D

A: Given,fXY(x,y)=6(x-y) ; 0&lt;y&lt;x&lt;1E(X)=34E(Y)=14

Q: For z € C, define Tz: CC by Tz(u) = zu. Characterize those z for which Tz is normal, self-adjoint,…

A: Given that: For z∈C, Define Tz:C→C by Tzu=zu. The objective is to verify the given statement. Now…

Q: Let z=x+iy ∈ C where x∈R\{1}, y∈R, and |z|=1. If w = (z+1)/(z-1), then show that Im(w) = y/(x-1).

A: Use the following formulae, to obtain the required result. Real part of a+ib=aImaginary part of…

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: Evaluate (2z + z – i) dz J|z-il=1

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Q: 1) Let f(z,y)- . Compute DS(z,y) where u- (4-9)

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Q: Suppose that w = f(r, s, t), where r = r(x, y), s = s(r, y), and t = t(x, y). Which of the following…

A: Solution is given below:

Q: et T E L(V,W), and U e L(W, X). Prove that UT : V → X is also linear

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Q: Let Y - Wei(2,2) Compute V(Y). O 3.1416 O .8584 (answer) O -2.1416 O 4.1416 Let Y ~ W ei(2, 2)…

A: The variance is calculated as follows:

Q: In(u cos v) and y = usin v. Evaluate and z at the point 2е" In y, x 3D (u, v) = (2, 7/4). Let z = du…

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Q: Given that w = f (u, v) And u = xz. , V = dw = X az aw aw Prove that Z - ду

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Q: [2 Lo 2. and defined T: R² → R³,by T(X) = AX. Let A Find the images under T of u = |E|, and v =

A: Given a linear transformation T:R2→R3 by T(X)=AX where A= 2002

Q: UE Mn X, y E C" are If orthogonal if and only if Ux and Uy are orthogonal. is unitary show that

A: Given  is a unitary matrix, where Note a  matrix  is unitary if its conjugate transpose  is its…

Q: * Let A E R"Xn, ĩ E R" \ {0} and A = 0. Prove that if the origin is stable if and only if ī is…

A: Given A∈ℝn×n,x¯∈ℝn\0 and Ax¯=0 To prove that the origin is stable if and only if x¯ is stable.  If…

Q: Let w = r = Uv, s = u - 3v. Use appropriate forms of the + s²' dw dw chain rule to find and in terms…

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Q: (6) I. adv, where E is bounded by the planes z=0, y = 0, =0, y+= =1 and +=1, as shown in the figure…

A: Given that,

Q: Compute F. Oszs V1-x2 –y? Let E be the hemisphere described by and F=Vz2 + x² +y² i + Vz² + x² + y²…

A: By Gauss divergence theorem:∬∂EF·nds=∭Ediv(F)dvhere givenF=x2+y2+z2( i^+j^ +k^…

Q: If S and T are normal linear operators satisfying ST* = T* S and TS* = S*T, show that their sum S+T…

A: I have used just definition of normal operator

Q: Let, T:R' → R';T(x,y,z) = (x + y+ z,2y+z,2y+3z) 2. Find the dimension of KerT and ImT

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

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Q: Let x, y E Rn be given. (a) If ||x|| = ||y|| = 1 and x y = 1, show that x = y. (b) If ||x|| ≤ 1 and…

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Q: 2. In A ABC, X is the centroid. A A If CW = 15, find cx and XW. W, B. If BX = 8, find BY and XY.

A: we know that  centroid is located 23 of the distance from the vertex along the segment that connects…

Q: Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y||…

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Q: 13. Let f(x, y, z) = xy+z², with x(s,t) = s², y(s, t) = 2st, and z(s, af/ds and df/dt %3D %3D

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Q: xy−5yz−7xz,x=st,y=e^(st),z=t^2 Compute ∂w/∂s(1,−2)=

A: The equation given as  w=-2xy-5yz-7xz , x=st , y=est ,z=t2. The partial derivative of the function…

Q: How to solve this?

A: We are given that x + y + z = 5 where x, y, z ∈ R. Now, we need to prove that x2 + y2 + z2 ≥ 5/3.…

Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.

A: Solution:- The given question is  Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find…

Q: For z ∈C, define Tz: C →C by Tz(u) = zu. Characterize those z for which Tz is normal, self-adjoint,…

A: Firstly, find out Tz*.

Q: Let f(x,y,z) = zIn(x³ycos(z)), find Z 3x² O In(x3ycos(z)) - ztan(z) 0 2 Y о 3z X af ila

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Q: Let P = {(z, y, 2) E R° | az + by + cz = 0} where (a, b, c) # (0,0,0). (a) Prove that (a, b, c) ¢ P.…

A: Given that P=x,y,z∈ℝ3 : ax+by+cz=0 where a,b,c≠0,0,0 (a) The objective is to prove that a,b,c∉P Let,…

Q: Let z, w e C. Clearly prove that z+w = z + w.

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

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: Let z, w E C. Show that zw = 0 implies z = 0 or w = 0. %3D

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Q: For x, y, z, w > 0, prove that (x/z)+(y/z)+(z/w)+(w/x)≥4

A: It should by x/y, instead of x/z

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: . Suppose that T e L(V) and U and W are invariant under T. Prove that U + W is also invariant under…

A: If U is subspace of V and T(U) is subeset of U then U is invariant under T

Q: 1. Let z, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1…

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Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to:

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Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).

A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…

Q: If X and Y are two independent RVs with f (x) = e*U(x) and f „(y) = e U(y) and Z = (X – Y)U (X – Y),…

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Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

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

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Q: Compute I ds over the path C : F(t) = (t, 2t,ť²) from (0,0,0) to (4, 4, 4).

A: The answer is given below:

Q: Let m e N and a, b e Z be such that (a, m) = 1 and (b, m) %3D = 1. Let h = 0m(a), k = 0m (b), and…

A: Let m∈ℕ and a, b∈ℤ be such that a, m=1 and b, m=1. Let h=oma, k=omb,  and  n=omab. We need to show…

Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: Let f(x, y, z) = x2y + y2z. Use the Chain Rule to calculate af /as and af /at (in terms of sand t),…

A: