If S is a subset of T , then u* (T) sµ* (S) ylgn C ihi O

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

A:

Q: A. If z=x + f(u) and u=xy. Show that: x+y- ax =X

A: Question are not correct... I will send this type problem

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 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: Let E = [-2, 3) U {−3, π}. Determine the following max D inf D interior of D boundary of D closure…

A: Solution:-

Q: Show that the Stein operator for Poisson P(Y = k) = is Tf(r) = Af(k + 1) – kf(k).

A: Given information: The Stein operator for Poisson P(Y = k) = λk/k! is Tµf(x) = λf(k + 1) – kf(k).

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

A:

Q: Prove that if w=f(x, y, z), x=r-s, y=s-t, and z=t-r then dw dw dw + + = 0. dr ds ôt

A:

Q: If S is a subset of T , then u (T) sp" (S)

A: It is Always True

Q: If S is a subset of T , then u* ( T) sµ* (S).

A:

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: Define T R → R by T (a, b, c) = (a – c, b+ c) Is T one to one? [ Type Y for yes and N for no. Is T…

A: T  can't be one-one because of domain and codomain but T is onto

Q: Let F(x, y,z)=xi + yj+zk, f(x,y,z)=||F(x,y,z)||. Prove that: Vf" = nf"-²F F v(In f) =

A:

Q: Q:3 If sequences (xn)&(yn) are both in normed space X and Xn - x & yn →y, then x, + Yn x + y.

A:

Q: Let, T:R' → R³;T(x,y,z)=(2x+ y, y- z,2y+4z) 2. Find the rank and nullity of T.

A:

Q: If Z; is i.i.d N(0,y²) and X1~ N(0,o²) be independent of all Z's. Let Xi+1 = pX;+Z; for all i = 1,2,…

A: From the given information, The provided information are as follows: Zi~i.i.dN0,γ2X1~N0,σ2Zi and X1…

Q: 3) Aşağıdaki fonksiyonların tanım bölgelerini bulunuz ve çizimlerini yapınız. Bu fonksiyonların…

A: Given That :   a) z=1+x+y-1+3x-y   , (x0,y0)=(1,2) b) z=sin(x2+y2)x2+y2, (x0,y0)=(0,0) To Find : The…

Q: 1) Find the norm of the following operators d) T:C[0,1] → C[0,1] by (Tx)(t) = f¿(t - s)*x(s)ds

A: Norm of operator gives the idea of size of any linear operator. Norm of can be found as .

Q: If the Wronskian W of f and g is 3e^(4t), and f(t) = e^(2t), find g(t)

A: Wronskian W of f and g is given by:

Q: Let v: DX be a net in X. Then a point xo X is a cluster point of a net v = {xa} if and only if there…

A:

Q: 2) Let u(xy,2) = でさす。R。 () Find He(tいり, "g(1,0,り、 Uy(1,0,1). ニ0. (k) Show that oty a22

A:

Q: 13. Let T, O E L(V, W). Show that rk(T+0) ≤rk(T) +rk(o)

A: We are given that τ,σ∈L(V,W) We suppose, w∈Im(τ+σ)   ....(1) So, there exists some v∈V such that…

Q: dz Let z-ay" – 4r, * = uv and y-v - 3u. Compute Ən (u,r)-(1,1) -

A:

Q: 10. Let X , j= 1,.., n, be i.i.d. r.v.'s such that E(X,)= µ, o'(X)=o', both finite. j' Show that E(X…

A: The normal distribution: A continuous random variable X is said to follow normal distribution if the…

Q: 14) Find the Jacobian of the tra nsformation. x=5u-v,y=Du+3v

A:

Q: 1) Let u = w² z³, where w = s?t, z = se-t. Find u when (s, t) = (1, –1).

A:

Q: Let T : V --> W be linear, b ϵ W, and K = {x ϵ V: T (x) = b} be nonempty. Prove that if s ϵ K,…

A: Given: Let T : V --> W be linear, b ϵ W, and K = {x ϵ V: T (x) = b} be nonempty The objective is…

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

A:

Q: Compute the Wronskian, W[y1, y2](t).

A: Let y1(t) and y2(t) be two differentiable functions in the independent variable t. Then the…

Q: In R* whire n eN, let こ and イ.ES":(tx € E),(ヨr >o)ud tlnt Br (x) CE lang the deginition 4 topelogs…

A:

Q: Example 3.8. Forx = 1,2,3 and y = 1, 2, let the joint pmf of X and Y be defined by I+y fx,y(r, y) =…

A: XY X=1 X=2 X=3 Total Y=1 2/21 3/21 4/21 9/21 Y=2 3/21 4/21 5/21 12/21 Total 5/21 7/21 9/21 1

Q: Let E = XE[0, + 0) } then Sup E Маx E- %3D %3D x+ O True False

A: In this problem we have to determine Sup E and Max E, and check Sup E =Max E is true or false.

Q: For G = S, state Question 11. necessary and sufficient conditions on T , a subset of S = {1, 2, . .…

A:

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

A:

Q: Define T:R → R' by T(x, y, z) = (x-5y+4z, y- 6z). a) Is T one-to-one? Justify your answer. b) Is T…

A:

Q: Let A: C [0,1]→C [0,1]. Prove that operator A is continuous reversible, find A. Ax() = x() + ja-m}xt…

A: Solution:- We have given operator A such that A: C[0,1]- C[0, 1] Also we must know that the inverse…

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

A:

Q: 2. Let U = {a + bx + cx2 + d³ e P3 (R) | a- 6+d3D0}, and let W = {a + bx + ca? + dx³ e P3(R)| a + 2c…

A:

Q: Let, T: R3 → R³;T(x, y, z) = (2x + y, y – z,2y + 4z) Find the rank and nullity of T.

A:

Q: ☺ RB=R defuid by T☺)- matria "A" it. T@)- A:). つレ- TV4 Let T: -3v-Jw ). Füd

A:

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: of E. 4. Let E CR be a bounded set. Prove sup E e Ë.

A: (4) Let E be a bounded subset of R  and let u be the sup E.  Then two cases arise-  Either u belongs…

Q: The joint pmf of X and Y is given in the following table. y P(x.v) 1 0.02 0.06 0.03 2 0.07 0.15 0.20…

A: Solution

Q: Exercise 4.11 Suppose m is Lebesgue measure and A is a Borel measurable subset of R with m(A) > 0.…

A: Given, m is Lebesgue measure and A is a Boral measurable subset ofℝ with m(A)>0.  To prove that…

Q: 5) Let Re(z) and Im(z) denote respectively t parts of z, show that:- 2)z+z= 2Re b) Z-Z= 2i Imn( z)…

A: Given

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:

Q: Prove that if w = f(x,y,z), x=r-s, y=s-t, and z =t-r then ôw ôw ôw + âr' as = 0. ôt

A: