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, a2 is greater than 0 but less and equals to 2, a3 is greater than 1 but less than and equals to 3. To show A is a bounded subset of R^3. and find the diameter of set A. and if the saying is correct"there exist vectors a,b in A, ‖a-b‖=diameter of set A. please Justify

Q: Q2) Let (A,T)be topological spaces; i=1,2,3. Then A, x A2 x Az is homomorphic to (A, x A2) x A3 I

A: Definition : Let X and Y be spaces, and let B be the collection of sets U × V , where U ⊆ X and V ⊆…

Q: Consider the collection of vectors --000 1 Is Slinearly independent? Carefully explain your answer.

A:

Q: A set W is defined as consisting of all the planes in R^3 that are parallel to the plane x+2y-3z=1.…

A: A set W is defined as consisting of all the planes in R3 that are parallel to the plane x+2y-3z=1.…

Q: ) Consider the space R^2 equipped with the sunflower metric. Identify explicitly the set of points…

A: The objective of the question is to identify the set of points in R^2 that form a ball of radius 1…

Q: 28. Find the unit vector in the opposite direction to 7 –j + k.

A: We will solve the following

Q: 3. Let A, B, and C be three distinct collinear points such that AC <AB and BC < JAB. Prove that…

A: Let given points be in order A-B-C. But then AC can never be less than or equals to half of AB.…

Q: What are the coordinates of the point on the directed line segment from (-1, –6) to (8, –3) that…

A:

Q: onil s 2 S = {v1,V2} = 4 5 7 8. a. Explain why S is linearly independent but is not a basis for R³.…

A: A basis for a subspace S of Rn is a set of vectors in S that is linearly independent and is maximal…

Q: Prove

A:

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: make an example and prove it about five vectors spanning R⁴

A: Given: Five vector spanning R4  We need to form an example and prove the given statement 'Five…

Q: 9. Let A=span{v = (-1,–1,2), i = Projau. (2,3,0)} and w (1,2, 3). Find

A:

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: d) The set of real numbers, with addition defined by x + y %3D х - у

A:

Q: Which vectors, drawn on a grid from one point (on the "cross-hairs") to another have integer values?

A: Y-component of A →…

Q: 28. Prove that if A and B are any nonzero vectors and C- BIA + JAB, then the angle between A and C…

A:

Q: Consider the vectors u1 = (1, 2, 1), u2 = (0, 3, 2) and u3 = (−2, 1, 1). Determine whether the set S…

A: The objective of this question is to determine whether the set of vectors S = {u1, u2, u3} spans the…

Q: If (X,7,) and (X,7,) T. - spaces, then (X,7,nt) is also a T,- space. GOOD LUCK

A:

Q: 5. For which value of x do the following vectors form a linearly dependent set in ¹ X₂ G

A:

Q: What are the coordinates of the point on the directed line segment from (3, 3) to (10,-4) that…

A: General formula

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: 22. Let v₁ = (1, 6, 4), v₂ = (2, 4, -1), V3 = (-1, 2, 5), and W₁ = (1, -2,-5), w₂= (0, 8, 9). Use…

A: Given vectors are Here observed that So we have each of .In other words ,

Q: (4) 2 What is the square of the (minimum) distance between W and P? Let W Span< = -2 be a plane in…

A: Given that

Q: (-4,2+i, 1), and y = (i, 5, 1 + i) be vectors in C. Compute (r, y), Let z = ||x||, ||y||, and ||r+…

A:

Q: Consider the empty set, i.e. X={ }. Which property of vector space is not satisfied and how?

A: A vector space is a set with a 0 element with two operations: addition and scalar multiplication…