2. Consider the topology 7, = {X,ø,{a},{b,c}}_on X = {a,b,c} and 1, = {Y,ø.{u}} Y = {u,v} . the topology Note that on {(a,u),(a,v),(b,u),(b,v),(c,u),(c,v)} is the product set on which the product topology is defined. Determine the following: XxY = a) II.'(x) b) II,'(0) c) II.'(a) d) II,'(b,c) e) II, (u)

Q: Let U=span u, ,ū2, ūz and Ü=span{ú, ,ú2,úz where ü,=(1,0,0,0), ủ,=(0,1,1,0), ủ,=(0,1,1,1) and…

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Q: Let the ordeced two bases of the spaces B be A=- (1,3) (E),L)} and B=fF3,2).(5,1)} ln the case, find…

A: We required to find the transition matrix from base B to base A Which is given follow

Q: Let v be represented by the directed line segment from (0, 0) to (3, 2), and let u be represented by…

A: Given that, v is a line segment from (0, 0) to (3, 2) So, v=(3,2) - (0,0)= (3,2)   Given that, u is…

Q: Theorem 23. If u, v E Q then we can find integers a, b, d with d > 0 such that u = a and v = d'…

A: By Division Algorithm we know that,               Let a, b be two integers with b>0. Then there…

Q: The closure of (-co0,2) in the left ray topology is A) (-c0,2) [B) (-0,2 C) R D) O

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Q: Let U​ =​{1, 2, 3, 4, a, b, c, d, e​}, E​ =​{1, 3, 4, c, d, e​},F​ =​{1, 2, b, c​}, and G​ =​{1, 2,…

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Q: Verify that {uq.u2} is an orthogonal set, and then find the orthogonal projection of y onto…

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Q: 20) Find two sets f polar coordinetes, (r, o),0LOL2 IT Por the point (6,6) in recten- gular…

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Q: 50. Find the vector from the origin to the point of intersection of the medians of the triangle…

A: NOTE :As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 1) Determine the projection of a= [5, -4, 8] onto b = [3, 7, 6].

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Q: Q/ show thet f(2) = 2+ Conformal maps 121= 1 ? on

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Q: 8. Which line does not lie on the plane r = (1,5,0) + s(2,-3,1)+t(1,−1,4), s,t € R? a. V = (1,5,0) +…

A: To Find: Which of the given lines does not lie on the plane r = (1,5,0)+s(2,-3,1)+t(1,-1,4) where…

Q: Find the norm of the projection of u onto a ( || proj,u || ) with the following: (a) u=(1, – 2). a…

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Q: Show that close ball Y in a metfic space (X,d) is a closed set also show that if (X,d) is complete…

A: Show that closed ball Y in a metric space (X,d) is a closed set also show that if (X,d) is complete…

Q: Let (X, T) be a topological space, AcX, then A'next (A) = 10 AO

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Q: Which of the following points is closest to (1,0, 1,0, 1, 1) using Hamming distance? O (1,1,1,1,1,0)…

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Q: Pargilelogram ABCD With Al-4,-3) BL-1, 4),C(5,66), D(2,-1) transiafe according to the roe (xiy)->(x…

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Q: and the projection pros

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Q: 18. Find the vector u in 2-space of length 2 that makes an angle 0 4.

A: A vector having length u→ and makes an angle θ is given by  u→ = u→cosθ i^ + u→sinθ j^

Q: Calculate the volume of the parallelepiped spanned by u = (2,0, 4), v = (2, 4, 2), and w = =…

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Q: erify that (u,,u2} is an orthogonal set, and then find the orthogonal projection of y onto Span…

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Q: let A be a set. A:=(a1,a2,a3) in R^3 such that a1 is greater than 0 but less than and equals to 1,…

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Q: 2. Find the midpoint of Segment AB, where Point A is at (-5,1) and Point B is at (15,8). O (5, 3.5)…

A: Mid point of a line segment is a point which is equidistant from the two endpoints of the line…

Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: 9. Ŵ Let U = (1, 4, 3), V = (2,1,1), W = (1,0,0). What is the dimension of the span of {U, V, W} ?…

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