Show that S {x€R* |2,• 24. • O} is/isn't %3D convex

Q: Solve the following inequality graphically in two-dimensional plane:y < – 2

A: We first draw y=-2 line

Q: Express K#S^2#T#2P as a connected sum of projective planes or as a connected sum of tori.

A: To express the given connected sum (of surfaces) in the required form

Q: (2) Consider the following LPP where a, b e R: maximize AT1 + br2 subject to 3r2 = 6 T1, 12 >0

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

Q: d. Consider the following convex optimization problem min fo(x) s.t. x EN where O C R" is a convex…

A:

Q: Find and plot the cubic spline S satisfying S(0) = 1, S(1) = 3, S(2) = 3, S(3) = 4, S(4) = 2 and…

A: %File Name: findSplineCoefficient.m %Define function function [ retCoeff ] =…

Q: Show that the problem B symmetric minimize || B A ll subject to Be R is solved by A + AT B= %3D

A: To show that the problem minimizeB∈ℝn×n∥B-A∥F subject to B being symmetric is solved by B=A+AT2

Q: Find the dimensions of the minimum-cost open-top rectangular tainer. (Let v* = 10 m³.) con-

A: Given. We need to find the dimension of a topless cuboidal container. Whose volume is 10m³ And…

Q: Find the Wronskian of a given set {yı, y2} of solutions of 7. (1 x2)y"-2xy' (a 1)y0, _

A: Consider the given equation.

Q: If A and u are nonzero Lagrange multipliers, VA? + µ² = 1.

A: If λ and μ are non zero Lagrange multipliers then we have to tell it is true or false  √(λ2 + μ2) =…

Q: Show that S= {xER*| x < 2x.} IS convex

A:

Q: Q 2. Consider the following LPP X1 + x2 - 4x3 + 0x4 + 0x5 + 0x6 X1 + x2 + 2x3 +x4 X1 +x2 - X3 -x1…

A: minimize   z=x1+x2-4x3+0x4+0x5+0x6subject to, x1+x2+2x3+x4                      =9  ---(1)x1+x2- x3…

Q: 1. Use agrange multipliers to find the extreme values of f(x,y)=2x²+ y on the circle x² + y² =1.

A: Here, f(x,y)=2x2+y and let g(x,y)=x2+y2, thus, the constraint is g(x, y)=1. So, fx(x, y)=4x; fy(x,…

Q: Write down (without solving) the dual LP problem. Minimize c =s+6t+u 9s -t+v23,000 u- v 21,000…

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Q: Solve the following LP: Minimize C= 2x+5y Subject to: x+2y 2 4 3x+2y2 6 x20, y 2 0

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Q: (b) If X is a normed line- ball M= {xeX:x≤1}

A:

Q: - Show that the area of the triangle whose vertices are the [x1 yi det X2 Y2 A - points (x₁, y₁),…

A:

Q: Use Lagrange Multipliers to solve the following: Maximize f(r, y, z) = 4x + 2y + z subject to z2 + y…

A: We have to maximize f(x,y,z)

Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

A:

Q: Which of the following points are collinear to (1,0) and (3,6)? Show graphically and analytically.…

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Q: Use the following graph of ) to estimate the solution(s) of Ax) = 0 for osxS6.28. 3.14 471 6 28 -1-…

A: We know the values of f(x) are given in the y axis, so y = f(x). y is the dependent variable and x…

Q: Show that the function f(x, y, 2) = (x² + y² + 2e**)4 is strictly convex on R³.

A:

Q: EX2 Compute the secand erder partial Jerivative Fx ち,ち~ and a)

A: " Since you have asked multiple  question we will solve first one for you. Please ask specify…

Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: 1 if i= j 0 otherwise. P:(c;) = 5 is a linearly independent set.

A:

Q: Solve the following inequality graphically in two-dimensional plane:2x + y ≥ 6

A:

Q: Find the bounded อน əx solution of อน 2 + U if U(x, 0) = 6e-3x. at

A: We have ∂u∂x=2∂u∂t+u  The initial condition is ux,0=6e-3x Now, ∂u∂x=2∂u∂t+u can be written as…

Q: Let f(r, y) = 5x-+ 2y + 4y- 8ay List the critical point:

A:

Q: Let a and b be nonzero and f(x, y) = (ax + by)e-x Show that if a ± b, then there are five critical…

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Q: Show that f10 fdx + gdy = S6 10 5a*y²dx + 2yx³dy is independent of path •(11,–7) ,-10) • (11,–7)…

A:

Q: Show that; is a linearly independent set in R3.

A: S=121,011,201 Let a,b and c be the scalar in R3. Then write the set in term of linear span.…

Q: The Canonical form of a hyperbolic PDE is F (ξ, η , u, ug , un ) %3D False True

A: To check the given statement is true or false. Given that the canonical form of a hyperbolic PDE is…

Q: Solve the following inequality graphically in two-dimensional plane:3x + 4y ≤ 12

A: We first graph 3x+4y=12 line We make a table for it x 4 0 y 0 3

Q: Find the pointof 5x²+2x²-3x conditionaliy and inflection of by giving the. yo pooper. Concave Conae…

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Q: Find the absolite marima and minima points between [o,u] gf y : * + 2dx' sunchion is porsbl.

A:

Q: Determine the convexity/concavity propwity of the following: (iii) U(x, y) = xªyB,where 0 < a < 1…

A: Here first make the hessian matrix and then find Z^(T)HZ and check whether it is negative or not…

Q: Suppose that T :C C is R-linear. Show that T is C-linear if and if T(iz) = iTz for all z.

A: First we describe the definition of C-linear function:

Q: (ii) Show that the quadratic function f(x)=x" Ax+2b"x+c with A = AT E R²x",bER",c ER is strongly…

A: Sol

Q: Let F1 and F2 be 4-dimensional flats in R6, and suppose that F, N F, # Ø. What are the possible…

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Q: Solve the following inequality graphically in two-dimensional plane:3y – 5x &lt; 30

A: We first graph 3y-5x=30 using a table  x 0 -6 y 10 0

Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4x + 2y + z %3D subject to 2²…

A: Here the number of constraints is one that is g(x,y,z)=x^2+y+z^2-1=0, and the objective function is…

Q: Find the unique fixed prbability vecter for the regular stochostic matrx A= ) 2 5 2 0 3 3

A: The following information has been given: The regular stochastic matrix is : A=311252033 We need to…

Q: Find the absolute maxluum of fr.4)=2y bject to the Constraint gixy)= x?ty²=/

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Q: ■ Show that the area of the triangle whose vertices are the [X1 У1 points (x₁, y₁), (X2, Y2) &(X3,…

A:

Q: Show that S = 2 is a linearly independent set in R³.

A: Given:     S = 121 , 011 , 201   To show that S is linearly independent set in R3

Q: Find the null space associated with the equations: 2x+z+w = 0 7x-6y–z–w-v = 0 -5x+4y+w = 0

A:

Q: Let fa) = x -1E Zs CxJ, wrte fX) as a produt of ireduclble polynomias as Zg.

A: Answer