Q3) Let L = Z* and |x ||= max {]x1 - x3l, x2l, 15x,1} Vx = (x1, X2, X3, X4) E Z*. Is (Z*, ) is a normed space?

Q: Q3) Determine whether V is a vector space with the following operations. If it is, verify each…

A: We have to solve given problem:

Q: How do you know that for all a, b, c, d: ax + bx will be orthogonal to cx? + d ?

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Q: Construct bijective maps (a) from [0, 1) to (0, 2]. (b) from R − {3} to R − {1} (c) from Z to Z −…

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Q: Find a condition on a, b, c so that (a, b, c)  ∈ R^3, belongs to the space spanned by →u = (2, 1,…

A:

Q: Q7) (a) Let X be a Banach space and R the usual normed space. Show that ||(z, a)|| = ||||+|al is a…

A: (a) Given a Banach space  and  the usual normed space, we want to show that the norm  is complete on…

Q: 20. Let V be an inner product space. Prove that (a) |||x|| - ||y||| ≤ ||x − y||. (b) (x, y) =…

A:

Q: 2. a. Sketch and/or clearly describe the region of integration. 3 V9-x2 3 yz dz dy dx 2²+y² -3 b.…

A: We will use basic of integration and geometry

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: (a) A¹\{1} (b) V(x+x) CA² (c) V(x2-x7,x3-x})\{0} CA³

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: let (2, m) be a meesurable space. then 1f f9: x LJare measural ble function, then -> ) f43 is mea…

A:

Q: If A, B are subsets of the topological space X show that Ext(AUB) = Ext(A)n Ext(B).

A: Given: A and B are subsets of the topological space X. To Prove: ExtA∪B=ExtA∩ExtB

Q: 5. If W is subspace, if A = : a. (A + B) is subspace these [8] € W and B = Non of above [8] € W,…

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Q: II. Decide which of the following are subspaces of corresponding vector spaces: C R?

A: Vector space.

Q: How is the nullspace N(C) related to the spaces N(A) and N(B), if C = [ A/B] ?

A: Given: N(C) is a nullspace and C=ABTo find: The relation between N(C),NA,NB matrix wise.

Q: 9) Suppose u, v € V, where V is an inner product space, and ||u|| = ||v|| = 1 and (u, v) = 1. Find u…

A: I have used the property of norm,  IIxII=0 off x=0

Q: Let V be an F vector space of dimension n. Prove that, for k≤n the vectors V₁, V2,..., Uk are…

A: Hints:   It is given that V be a vector space of F of dimension n. Then we have to prove that  vi's…