In a motric space, is the closed ball B[pic] closus of the opon ball B (pir)?

Q: Suppose v1, V2,..., Vm E V. Prove that {v1, v2, ..., Um} = (span(v1, v2, ..., Um))-.

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Q: Prove that the open ball B(a,r) is a subset of the interior of the closed ball C(a,r)

A: Given that Ba,r is an open ball of radius r and centered at a. Then a∈Ba,r                ...... (1)…

Q: 18. Determine whether each of these functions is a bijec- tion from R to R. a) f(x) = -3x + 4 b)…

A: As per guidelines, we will solve first three subparts of the question. a) Given function is fx=-3x+4…

Q: (2,3) is te i చాంబ! Under a ro dediona Identidy three distinct point that Cald be the center & of

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Q: S ⊂ R3 be the set consisting of 2 points (1, 2, 2) and (1, 2, 3). Find the annihilator of S. Show…

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Q: (b) Let the distance between two adjacent planes parallel to the plane (hkf) in the direct lattice…

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Q: 1. Let d, be a metries on Xo and let the function a: X x XR defined be dr. y) dis. y)= prove that…

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Q: distance Q.2A) ((q,x+ 92y+ 93z = M, ,41x + 92y+932 = M2)) |M, – M2| Prove the between to planes…

A: Let the point (x1,y1,z1) is on plane 1 and the point (x2,y2,z2) is on plane 2. As we already know…

Q: 1) this case? Consider V = C as a R vector space. What is the complexification Vc in

A: Given that: V=C as a R vector space. The objective is to determine the complexification Vc. Now…

Q: Find the value of z in rhombus FGHI. z+48° 5z H 3D = Z F.

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Q: For which of the following space the unit ball is weakly compact a) ℓ2; b) ℓ1; c) C[0, 1]; d) ℓ∞; e)…

A: We are given four spaces. We asked to check in which space a unit ball is weekly compact.Weekly…

Q: Let (X, T) be a topological space and A,B CX- ConstYuct the general Yelation between Fr (IntlA) and…

A: For any subset B of a topological space X , Frontier or boundary of B is defined as  Fr(B) = CL(B) -…

Q: Find a bosis for the nullspace of the morkit 5-23 (-12 -2-10 4 -6J

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Q: Q. Let (X, B(R), µ) be a Borel measure space. If AnB=¢, BnC = 0, u(AnC) = 0. Determine µ(AUBUC).

A: Measure theory

Q: Examplei Let M be on elliptic parobolbid x= y?4z? a) Find klu) at P= (4, to 12 2. b) Compute the…

A: Given equation of elliptic paraboloid is x=y2+z2              (i) Differentiating x w.r.t y and z…

Q: Let u = and v = Show that is in Span (u, v} for all x and y. y -1 5

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Q: Q. Let (X, B(R), µ) be a Borel measure space. If AnC = ¢, BnC = ¢, µ(An B) = 0. Determine µ(AUBUC).

A: Measure theory

Q: 4. Find the center of (a) V; (b) Q8-

A: We have to find centre of following groups: Definition: Let G is a group then centre of G denoted by…

Q: What is the dimension of the vector space P°?

A: The dimension of Pn is n+1

Q: Use Pitman’s formula to compute the MREE of the location parameter in the uniform family U(θ, 1 +θ)…

A: In the given problem, we are dealing with a random sample (X1, X2,..., Xn) where each Xi follows an…

Q: 1. Find a parametrization of the line segment L from -2 to -2 + 2i. 2. Find the image of L under the…

A: We will find the equation for L and the image of L under w

Q: Consider a dihedral groop Dy=<agb: asb= (abj=1 Ds cuss all Dy and verify Subgooups of "Dy=…

A: See answer below.

Q: Determine whether R is reflexive, irreflexive, asymmetric, antisymmetric, transi tiwe.

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Q: 3. For which of the following space the unit ball a) (2; b) e1; c) C[0, 1); d) l; e) L³[0, 1]. In…

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Q: Q. Let (X, B(R), µ) be a Borel measure space. If An BnC t6determine µ(AU BUC). 1 Add file

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Q: Let A = Find necessary and sufficient condi- d tions for A to be diagonalizable.

A: Given:         A = abcd   To find:      The necessary and sufficient conditions for A to be…

Q: 3.3 Let r1 and r2 be distinct points in the metric space (S, d). Verify that there are open balls S,…

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Q: for fuzzy sets A, B and C, (AVB)vc = AVIB VC). (Ал в) лс - АЛ(ВЛС). (A V BF = A“AR prove that AA CB…

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Q: Show that both ℝ and ℝ2 may be covered by countably many open spheres.

A: We have to show that  and  covered by countably many open balls.

Q: a Find the distance from the point pC,,1) to the plane 2K -3y+77=1

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Q: In the frieze group F7, show that zxz = x-1.

A: As per the question we are given the frieze group F7 which consists to four group operations : Tx :…

Q: is x=0 considered a vertcial asympptope?

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Q: Multiple Choice Identify the choice that best completes the statement or answers the question. Which…

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Q: Usually there will be exactly one hyperplane in Rn that contains the n given points x = 0, a1, ... ,…

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