Let 9-(a: a€R}, then T is Borel algebra.

Q: 8.0. If x-(x,, X, ...,%)«R', define [xL by Prove that xJkL is a norm on R'. N I|} dns - x]

A: We will solve the first question highlighted in yellow. If you want the second question to be…

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A: Given that  X = {m, n, p, q} and ∑=ϕ, X, {m}, {n}, {p, q}, {m, n}, {n, p, q}, {m, p, q} we have to…

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

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Q: Let 7={a: a€R}, then 9 is Borel algebra. ylgn ihi

A: True

Q: (a) Pieve that f 2 and Ź are segma algebras s over X th

A: Definition of Sigma Algebra: A Collection ∑1  of subsets of an arbitrary algebra if : (1) X ∈∑1…

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Q: Please solve 4,5,6,7 The Borel o-algebra on Ris generated by any of the following collections of…

A: As per the company policy, in a multipart question like this, we can solve only the first two…

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Q: is bijection. Do the same thing with Z,.

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Q: give example is not To-SPace about to folegical SPace

A: We have to find a topological space which is not t0.

Q: Theorem: Proper ies of Transposes 3.) %3D

A: If we take transpose of transpose matrix, the matrix obtained is equal to the original matrix.…

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Q: let (RiZ) be the usual top on et B-1 ineN] Find B.

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Q: ) Assume (X,A) is a Ealgebra and ld ycx be an anbitrary subset. Show that the Pami ly of sets…

A: σ-algebra: a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X, is closed under…

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Q: FOR ANY TWOCOMPLEX NUMBERSZ, ANDZ,,PROVE THAT |Z|+|Z,|=,(Z, +Z,)+ /Z,Z» +÷(Z, +Z»)- Z,Z, .

A: for two complex number Z1 and Z2 prove that Z1+Z2=12Z1+Z2+Z1Z2+12Z1+Z2-Z1Z2

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Q: Show that R³ is spanned by S = {(1,1,1), (1, – 1, 0), (0, 1, – 1)}.

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Q: Use membership table to prove (AunionB) – C = (A – C) union (B - C).

A: We need to prove the following statement using membership table. A∪B-C=A-C∪B-C

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Q: Let a ER which expressions are part of the Borel o algebra, B(R) they are correct? and give the…

A: The main objective is to determine the correct option.

Q: 32. Show that, in a normed space, x x implies -(x1 ++Xn) → x.

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Q: Let -{[:);}--{:)[:} -{{)}} Both B and C are bases for R2. If {x}s =: -[:], what is {x}c?

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Q: uppose A is a diagonali= . Would this be true if

A: Given, A is a diagonalizable n x n matrix whose eigenvalues are all 1 or -1.

Q: How can I prove this?

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Q: Let 9={[a, ): a€R}, then T is not Borel algebra. ulgn O ihi O

A: Solution  False Detailed Explanation

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A: Given: u→.v→=2, v→.w→=-3, u→.w→=5, u→=3, v→=2, w→=2 we know that u→-2v→2-2w→.w→ is given by…

Q: Dimension of ker A is Rank of A is

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Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: topological spaces X and Y,

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Q: 2. Let W = Span {u1, u2, uz3, U4, U5, U6}, where 4 1 , U5 = Uj = U2 = u3 = ,u4 = U6 = 2 2. 4 What is…

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Q: 8. Show that A is Hermitian if and only if A = B - C with B,C positive.

A: A is Hermitian if and only if A=B-C with B, C positive.

Q: Show That R is Banach Sface.

A: To Show -

Q: Let J={(a,∞): a€R}, then T is Borel algebra. صواب İhi

A: True

Q: Let A = %3D

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Q: let FQ) = -2Xidefined on [14], then UC Pmif) =

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