Let r, y E R". Using the triangle inequality ||r + y|| < ||1|| + ||y||, show that r|| – ||y||| < ||r – y||, where || - || represents the Euclidean norm.

Q: Solve the following inequality graphically in two-dimensional plane:y &lt; – 2

A: We first draw y=-2 line

Q: Exercise. Is it possible for a metric space (X, p) to contain more than one point and be such that…

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Q: 3. Consider the Cauchy-Schwarz inequality. That is, for u, v E R": Use some reasoning, or do some…

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Q: ||x||3 < ||x||1|||| VI 22

A: As it is known, L2 norm of x is given by x2=∑i=1nxi21/2 L1 norm of x is given by x1=∑i=1nxi L∞ norm…

Q: Prove the following theorem in neutral geometry: If there exists a constant c and a model for…

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Q: Lemma 2.56 Let (X,T) be a topological space, (M, d) be a complete metric space and BC(X,M) := {f €…

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

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Q: Show that X is Hausdorff if and only if the diagonal △ = {(x, x)|x ∈ X} is closed in X × X.

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Q: 6. Use Cauchy-Schwartz Inequality, Ju· v| < ||u|| |v||, to prove the Triangle Inequality: ||u+ v|| <…

A: To Determine: Use Cauchy-Schwartz inequalities,                                  u.v≤u  v To prove…

Q: = 0,1] and d be the usual metric, d(x, y) = a -y %3D en d can not induces a norm on X True False

A: the usual metric d(x,y)=|x-y| usually induces the norm.

Q: Let X and Y be two T, spaces, then X×Y. :is

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Q: Let X = N and d be the usual metric, d (x, y) = |x – yl then d can induces a norm on X True O False…

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Q: .Six equal rods AB, BC, CD, DE, FE and FA are each of weight W mnd are freely jointed at there…

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Q: My question is why is norm defined like this please explain 2 | U | Le() = inf 1B>0:√ [(x) [P(x) do…

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Q: Show that the closed interval [0, 1] and the unit circle S' = {(x, y)|x² + y² = 1} cannot be…

A: Suppose there exist a homeomorphism f:[0, ∞)-----&gt;R then restriction of f f|[0,∞)\{0} : [0,…

Q: 4. Prove the Triangle Inequality: If v, weV, then || v + w ||<|| v || + | w || -

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Q: (b) Show that x. y < ||x|| ||y||- [Hint: If x, y # 0, let a = , 6= and use the fact that ||ax + by |…

A: Given that, Euclidean metric d on Rn is defined as d(x,y) = || x - y || for x, y in Rn Part(a): Let…

Q: graph the inequality on a coodinate plane x &gt; with line under it 2

A: To graph the given inequality x≥2.The equation x=2 has a graph that is a vertical line with all…

Q: Where x = (X1, X2) E R². 3- N: R2 - → R defined by N(x) = /x1² + x2² is a norm on R². (x1, x2) E R².…

A: Let X=(x1,X2)€R^2

Q: Prove that: 1. (R, |. |) is a complete metric space. 2. (Q.I-1) is not complete metric space.

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Q: which axioms for a finite projective plane are also valid in Euclidean geometry? which are not?

A: A finite geometry is any geometric system that has only a finite number of points. The familiar…

Q: Let X= [0, 0 ), and defined d as d(x,y)= e(xy) then verify all four condition of metric space

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Q: If (X.r,) and (X,r,) are T.-spaces, then (X.r,nr,) is also a T,-space. GOOD LUCK

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Q: (a) Prove that the metric space (2,11) is complete,

A: Complete Metric Spaces:- A Metric Space (X,d) is said to be complete iff every Cauchy sequence in X…

Q: b)use Cauchy Schwarz inequality to show that if Let u = and v = inequality to show that a² + b?

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Q: In the Triangle Inequality of Euclidean n-space: Prove ||x - z || <= ||x - y|| + ||y - z ||…

A: The triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle…

Q: . Six equal rods AB, BC, CD, DE, FE and FA are each of weight W and are freely jointed at there…

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Q: e have to prove that constructed geometric object indeed satisfies three condit

A: To show that given a projective plane P, an affine plane constructed from P denoted as Aff(P) is…

Q: Let x(bar) = (3,-5,2,1,-2) element of R5. Find the norm of x(bar) using the usual norm on R5

A: The norm of x is the distance between a point x to the origin.

Q: Q7: Prove that ( IR", ||·|| ) is complete metric space.

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Q: 2.2.7. Prove the full triangle inequality: for every x, y E R", | |æ| – |y|| < |x± y| < |æ| + \y]-…

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Q: 3. Consider the Cauchy-Schwarz inequality. That is, for u, v € R": Use some reasoning, or do some…

A: We have to prove ∑i=1nuivi≤∑i=1nui2∑j=1nvi2 Since we know the Holder's inequality…

Q: show that d connot be obtained from a norm.

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Q: .Six equal rods AB, BC, CD, DE, FE and FA are each of weight W and are freely jointed at there…

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Q: Q7: Prove that (R", ||-|| ) is complete metric space.

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Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: Prove that Ix I - I y I &lt; Ix - y 1-Hint: Apply the triangle inequality to y and x - y.

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Q: Show that the set of all real numbers constitutes an incomplete metric space if we choose d(x, y) =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Show that Z[V-2] is a Euclidean Domain with respect to the norm N defined by N(a + bv-2)=a? +2b?.…

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Q: Show that the set of all real number constitutes incomplete metric space an we choose doxoy) = Itan'…

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Q: prove with a table if x → y then xor y xor y = y

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Q7: Prove that ( IR", II-||) is complete metric space.

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Q: the usual metric space defined by  d(x,y)= x-y prove the four propertis of metric space

A: Applying four properties to this metric

Q: 2. Does d(x, y)= (x-y)? define a metric on the set of all real numbers?

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Q: An Elliptical norm for R2 is defined by + 4u2, where x = (1,u). (i) Prove that l is a norm for R2…

A: This is a problem of Functional Analysis.

Q: I. Solve using De Moivre's Theorem. Given that z is not real number and z = 1, show that w = z-1 z+1

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Q: Theorem. A rectangle R with side lengths 1 and x, where x is irra- tional, cannot be “tiled" by…

A: Without using the concept of linear algebra you can proof this. Let length of rectangle= 1 Unit…

Q: Show that the real number R with d(x,y)=|x-2y| are not a metric space

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Q: Find a bijection between the interval (−1, 1) and R.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.