Let A = {2, 4} and B = {1, 3, 5} and define rela- tions U, V, and W from A to B as follows: For every (x, y) E A × B: (x, y) E U means that y - x> 2. (x, y) E V means that y-1 = 5 W = {(2, 5), (4, 1), (2, 3)}. a. Draw arrow diagrams for U, V, and W. b. Indicate whether any of the relations U, V, and W are functions.

Q: Let X {1,2, 3} and Y {3,4}. Define f : X → Y as follows: = f(2) = 3 and f(3) = 4. Draw an arrow…

A: We will draw the arrow diagram for function mapping from set A to set B.

Q: Form 2 of the chain rule. Do the following problems: A. Let z = u² + v²; u = 2x + 7, v = 3x + y.…

A: To apply chain rule for this problem, we first need to identify the composite functions involved.…

Q: 1 Let f(z) = ((z -3i)² + 9)ez-3¹. Evaluate f f(z)dz, where C is |z − 2i| = 2, positively directed.…

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Q: 2) Use Green's Theorem to compute f F df where F= (3x +4y)i + 2xyj and C is the triangular path from…

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Q: Consider the function d: R² × R² → R defined by {} d(x, y) = min{|y2x₂, 1} if x₁ = y₁ otherwise, 1…

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Q: T(а, b, с, а, е, ) T(f, e, d, c, b, a) ' T(e,f,d,c, b, a) Τ(α, e,c, d, b, ) Τα,, b, d, e, f) Т(е, f,…

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Q: 6. Is the set S {(2, 3, 1), (1, 2, 1), (-2, 3, 3)} C R³ linearly %3D independent or dependent?…

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Q: 18. Show that u = [2.-5.15] is orthogonal to v = [20,–1,–3).

A: From the given problem:   u→=2,-5,15 ; v→=20,-1,-3   As we know that two vectors u→ & v→ are…

Q: If f(r, v)= +y-2y, find fa (2, 1), f (2, 1), fay(2, 1) and fy(2, 1).

A: Given a function f(x,y)= x3+x2y3-2y2 Now, fxx= ∂2f∂x2=∂∂x∂f∂x fyy= ∂2f∂y2=∂∂y∂f∂y…

Q: Consider the function d: R² × R² → R$ defined by [min{\32 - x₂, 1} if x₁ = y₁ 1 otherwise, d(x, y) =…

A: A metric on a set X is defined as a function d: X×X→ℝ which satisfies the following conditions:…

Q: Q2):- Find Y[Z] of signal Y[n]=(Cos wn). U[n]

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Q: 2. We showed in class that EL (: - T)(y: – 9) can be written as a linear combination of ys: B1 = Gi…

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Q: 4. Define the function T: R² → R as 1 T(v) = Av = |-2 4 V2 %3D -2 a. Find T(2, 4). b. Find the…

A: We need to find pre image.

Q: Suppose b, c E R. Define T: R³ → R² by T(x, y, z) = (2x − 4y + 3z + b, 6x + cxyz). Show that T is…

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Q: For all u and v in R" with u + 0, show that u is orthogonal to v – u•v

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Q: 5- Suppose that the vectors x = (1, –1,1), y = (1, –1,2), z = (2,2,0) in R3 then A: x is orthogonal…

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Q: Let G : R? → R³ and F : R³ → Rª be defined by G( (x, y)) F( (a,b, c) ) (x +y, x – y, 2y) (a + b+ c,…

A: Given G:R2→R3 is defined as Gx,y=x+y,x-y,2y Also,  F:R3→R4 defined by Fa,b,c=a+b+c,2a+c,b+2c,a+b.

Q: Compute the value of ( G. dL for G = 2ya, with A(1, -1, 2) and a) straight-line segments A(1,-1, 2)…

A: Given the line integral ∫APG·dL for G=2y,0,0 with the initial point A1,-1,2 and P2,1,2 using the…

Q: Let I = ff, (a2 – y?) dæ dy, where D = {(a, v) : 1< *y < 4,0 < a – y < 6, # 2 0, y 2 0} Show that…

A: Given: I=∫∫D x2-y2 dx dy where D=x,y:1≤xy≤4,0≤x-y≤6,x≥0,y≥0 .

Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: uppose that w = f(x, y, z), where z = r(u, v), y = y(u, v), and z = z(u, v). 'hich of the following…

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Q: Given u = (0,1, -1,2) and v = (1,1,3,0) find ||u + v||

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Q: Find the values of w, x, y, z and Dx, using Cramer's Rule x + y + z + w = 13 2x + 3y - w = -1 -3x…

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Q: EXY] = E[X]E[Y]. 1}) and U~U({-1,1}) are independent. Let Y = XU. e uncorrelated. e not independent.

A: *Answer:

Q: Let Compute дw -(-2,-2) = -(-2,-2) = მs дw St W = 2xy - 2yz + 3xz, x = st, y = est, z = t² =

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Q: If F(x, y, z) = (sin x + 2) i+2xz j+ (e-x) k and the path C is the line segment from A(1,2, 1) to…

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Q: If A%3 2x3 -Зх +2:х € [О, 2) then in (R, T,), A %3D а. [-3, 1] b. [-1, 1] с. [1, 3] С. d. [0, 4] e.…

A: Open sets and Closed sets: The sets in topology τ are called the open sets of the topological space…

Q: 4) Verify that Green's theorem is true for f,xy?dx – x²ydy ,where C consists of y = x² from (-1,1)…

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Q: Je and ди dv Je (in terms of u and v), using the following chain rule formulae: evaluate

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Q: T: P2 → R³ defined by T(a + bx + cx²) = (a + 1,6, c). T: R5 → R² defined by T(x1, x2, x3, X4, X5) =…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Let W(s, t) = F(u(s, t), v(s, t)) where u(1,0) = -2, u, (1, 0) = 8, ut(1,0) = -4 v(1,0) = -3, v.…

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