In R4, let S = span{(1, 1, 1, 1)T ,(1, 2, 1, 3)T }. Find S⊥.

Q: Show that the subset of R2 given by {(x, y) E R² : xy 1, x > 0} is closed.

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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: a u, (00) = Utt , и (0, t) — 0, и (т, t) — 0, (t>0) и (х, 0) %3D0, (0<x<n, и, (х, 0) %3 * (т—г),…

A: We need to find the solution to the threshold problem in the next wave equation by the variable…

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

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Q: Let, T: R' → R';T(x, y,z)= (x+y + z,2y + z,2y + 3z Tost uhothor the troncfCormotion T is linoer

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Q: a. Show that Ø, R E T. (by definition of Topology)

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Q: If A = x a, – zy a,, evaluate § A · dī around the path L defined by 0 < x < 2,0 < y < 1 as shown in…

A: Stroke's theorem:         It is also known as Generalized stroke's theorem. It states that the…

Q: Consider j1,ỹ2, ỹ,ER° and that ỹ,+y;+ÿ;=0. For Î=span{ÿ, ,ÿ and Y=span{ÿ2, ÿ}, show that Ý=Ỹ.

A: Given y1→, y2→, y3→∈ℝ5 such that y1→+y2→+y3→=0. Let Y^=spany1→,y2→ and Y~=spany2→,y3→. To show…

Q: Let (X, M, µ) be a measure space such that uX = 1, and let f : X → (0, 1). Show that u) / fdµ 2 1

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Q: Let →a=⟨3,1⟩ and →b=⟨1,0⟩. Find the projection of →b onto →a. proj→a →b=

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Q: If U = span {x, y, z} in Rn, then show that U = span {x + tz, y, z} for all values t∈R.

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

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Q: Show that the subset of R2 given by {(x, y) E R² : xy = 1, x > 0} is closed.

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Q: If there exists open ball B (a, r) such that B (a,r) nG = Ø then a is not limit point of G True…

A: TRUE

Q: What are the ASSUMPTIONS for t?

A: A t-test can be used when the hypothesis is concerned with the population mean and the population…

Q: (a) Find the length of the projection of w onto v given that w = (4,7) and v = (1,1).

A: Given: w=4i+7j, v=i+j we know that projectionp→ of w onto v is given by p→=w.→v→v→2v→

Q: Find the family of orthogonal trageclarnes fo he for

A: Given that            y3 = k x5 Here we have to find the family of orthogonal trajectories to the…

Q: 3. Find all the fixed points and classify cach of them: f(r,u) ryev,

A: Solution:- Fx,y=xye-x2-y2 Put Fx=0 and Fy=0 Fx=e-x2-y2y-2x2=0and Fy=y-2y2 e-x2-y2=0 So,  0,0,12,12,…

Q: {[: :}[: }} 1 2 1 0 1 -1 1

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Q: Let r(t) = ⟨t, t, t⟩. Compute r'(t) and interpret the result.

A: rt=t, t, t

Q: How many points need to be in a set in R° to guarantee that the set is affinely dependent? А. 11 В.…

A: According to the given information, it is required to tell the number of points in a set R9 to…

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: (f) The set B = {(x, y) E R² : x² + y² < 1} as a subset of R? with indiscrete metric is…

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

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Q: If there exists open ball B (a, r) such that B (a, r) nG=Ø then a is not limit point of G

A: To check whether there exists open ball B(a, r) such that B(a, r) ∩ G= ∅, then whether a is not…

Q: Let F(x, y) = (x, 0). Prove that if C is any path from (a, b) to (c, d), then F dr = 3 – a²)

A: Consider the provided information, Let Fx,y=x,0. Prove that if C is any path from a,b to c,d then…

Q: Compute the dimension of V,(Tỷ – Tỷ, TẬT, – T†T,) C P³.

A: Given that X=ϕ is a topological space. We have to compute the dimensions of the following.…

Q: Let (X, M, u) be a measure space wE

A: Given, (X, Μ, μ) be a measure space where μ is a probability measure. Assume thatf, g : X→ℝ are…

Q: Let T={[a, ) : a€R}, then T is not Borel algebra.

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Q: Let T={[a,0) : aER}, then T is not Borel algebra

A: Given a statement

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: 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: Which of these best describes T?

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Q: For every ,x, y E R, let p(x, y) =| x² – y² |. Is p a metric -

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Q: Let T={(a, 0): aER}, then T is Borel algebra.

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

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

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Q: Consider R? and R3 with the Euclidean (c) norms. Compute || T || for T : R2 →R3 defined by T (x1,…

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Q: et whose A = T be standard matsix teans bormaton is the lineas 2. 3. Does maps R3 onto R4? s Ta one…

A: Given that T is a linear transformation whose standard matrix is given by A=203032005000. We have to…

Q: Let X = R, and M = {0}, then span (M) = %3D %3D OR O {0}

A: If, M = {0} then, span(M) = {0}

Q: Let K = Span{ t-t, 1+3t}, then dim K = %3D

A:

Q: Consider the space L'[0,1]. Let p(f) :

A: Given, pf=∫1234f212, f∈L20,1. Standard L2-norm is f2=∫01f212

Q: Let F(x, y, z) = (z, x, y), ar (0,0,0), (0, 1, 1), vertices are ar

A: Introduction: Stroke's theorem is simply a higher-dimensional version of Green's theorem. The line…

Q: In each part, explain why the set S is not a spanning set for the vector space V. (a) S = {t³, t²,…

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Q: Let A EMn (R) be given. If 11x11 = 11yll = 1 and x •y = 1, show that x=y

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Q: Let X= (3, 5] u {6,7,...} and A= {5,6,7} and metric defined on X as d(x,y) = |x - y|

A: Note: As per bartleby instruction when more then three questions for subpart is given only three…

Q: An Elliptical norm for R2 is defined by + 4u2, where x = (1,u). (i) Prove that l is a norm for R2…

A: This is a problem of Functional Analysis.

Q: If u and v belong to the span of S, so does u+v

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Q: If e-ispure imaginary W hat Restriction is placed on z?

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Q: (f) Find the length of the projection of i onto ū.

A: Given