Suppose that you have two sets, and you know that both sets are convex. Proven that the intersection of those two sets is also convex.

Q: Explain in word what are the possible consistent and inconsistent system for 2 lines planes?

A: The conditions for the consistent system of equations can be explained as follows:

Q: Show that the set S= {(1, 2, 1), (3, 1, 5), (3, -4,7)} u de nendent where. SCV (B). is linearl

A: We need to find scalars c1, c2, and c3, not all zero, such that   c1(1, 2, 1) + c2(3, 1, 5) + c3(3,…

Q: 4. Prove that if A and B are convex sets, then AN B is also convex.

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Q: Show that the following set is convex: with A € ST C₁ = {x R¹|x Ax ≤ 1},

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Q: Explain in word what are the possible consistent and inconsistent system for 3 planes?

A: To explain: the consistent and inconsistent system for 3 planes.

Q: { O True O False The set 5 1 4 -4 1 -3 5 is linearly independent.

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Q: 3 Let A = -6 -1 -2 and v = -6- -2 3 Av = -6 2 -9 Ex: 5 s v in null(A)? Select an option

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Q: nis question we prove that certain sets are not convex. each of the following sets, give the…

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Q: Nancy's psychology teacher will give her a course grade that is the maximum of her Scores on two…

A: The convex preferences are concerned with averages and not maximum or minimum.

Q: 8.) the art gallery theorem does not tell us how many guards are needed to guard museums that have…

A: Feel free  to ask for further explanation.

Q: Problem 4. Which of the following sets are convex? (You need to justify your answer with clear…

A: Ans- (a) The set of points closer to a given point than a given set is convex. To see this, let x…

Q: 3. Let å1, åz, åz be three nonzero vectors in R2 and let b1, b2, bz be three real numbers. Consider…

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Q: The boundary of a set is equal to the boundary of the complement) True or false

A: (The boundary of a set is equal to the boundary of the complement) True or false

Q: 3. Use the definition of convex sets to answer the following: (a) Show that if the sets S and T are…

A: As per guidelines, I can do only first three subparts of the question.

Q: For the convex set C = {(z,9)+ 13 y.0 < 2.0 < y } (a) Which points are vertices of C? (52/9,35/9)…

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Q: 1. Let PC R³ be the convex polyhedron with only the following four extreme points: (0,0,0), (0, 1,…

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Q: 6.   Choose the point or points that are local minimums.

A: Approach to solving the question:A point x is said to be a local minimum, if there exist an interval…

Q: Determine whether the given set is linearly independent.

A: We will check that given set is linearly independent or not using definition of linear independency.…

Q: Choose the correct option. The planes have infinite points common among them if -> (a) p=2,q∈R…

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Q: Show that the set given in the image below is non convex. Please prove the result mathematically…

A: A set is said to be convex if for any two points in the set the line segment joining those points is…

Q: Exercise 4.6. Decide in each of the examples what kind of ordered set it is, poset, strict poset,…

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Q: Use a graphing calculator to find the shape of y = ex. Determine its concavity or convexity using…

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Q: Don't  give AI answer  plz give correct answer.  Prove that vertex v is an articulation point if and…

A: The objective of this question is to prove that a vertex v in a graph is an articulation point if…

Q: If D(L AOB) states the set of points located on the OA side containing point B and the OB side…

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Q: 2. Prove the following implication: strong convexity → strict convexity → convexity. Is the converse…

A: Sol:- The implication "strong convexity implies strict convexity which implies convexity" can be…

Q: This graph shows the number of visitors, in thousands, to a museum each year. Museum Visitors 24 22…

A: Given graph is Here x coordinate shows year and y coordinate shows the number of visitors(in…

Q: If minimum observation is 46.8 and maximum observation is 192.4, number of classes is 6, then the…

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Q: d) How could you calculate the surface area of any cube? SA cube

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Q: A and B be two sets, each one of them having a minimum. Assume that A n B is not ty. Then An B has a…

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