Let A E R2x3, be R². Determine whether or not S = {x R³ | Ax=b, x₁ ≤ 0, x₂ ≤ 0} X2 sa convex set.

Q: ercise 6.67. Let E be a subset of R having at least two points. Pro- owing are equivalent:

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Q: 1 Determine whether or not the three given points le on a ne A (1,1,2), B(-1,-9, 3), C (3,2,1) 2.…

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Q: Draw a sketch of the following subsets of R2. {(x,y): x² +y² ≤ 1}.

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Q: Let A = the set of straight lines in the xy-plane. Let a L b mean “line a is parallel to line 6”.…

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Q: Indicate whether the following statement is true or false ? 1. If S = span{u1, U2, Uz}, then dim(S)…

A: If Span u1,u2,u3 then dim (S)=3 the  dim S=3 if S is spanned by u1,u2,u3 and  u1,u2,u3 are linearly…

Q: Consider the following linear map T: P3 → P3 defined as follows: T(ao + a1x+ azx² + a3x³) = ao +…

A: For T to be an isomorphism we must check that it is one one and onto both. And we can check it by…

Q: Let vị = V2 = V3 V4 and -[1} Confirm that p = V1 +v2 + ¿v3 + ¿V4 and vị – V2 + V3 – V4 = 0. Jse the…

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Q: get the following sets {(x, y) : x ∈[1, 2], y ∈[1, 2]} and {(x, y) : x = 2, y ∈[0, 1]}

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Q: Exercise 2.29. Pick several different subsets of R, and for each one, find its interior and boundary…

A: Suppose X,I is a topological space and A⊆X. Interior of A, Int(A) is defined as the union of all…

Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

Q: Solve number 1

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

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Q: Let S = {[x y z] | 3x + 2y + z = 0} . Write the set S as the span of a set of two vectors in R 3

A: Let (x,y,z)∈Sthen 3x+2y+z=0                          z=-3x-2yTherefore,…

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

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Q: Find a topology in which the point x = 5 is an open set.

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Q: Let A € Rmxn and suppose that the rank of A is m where m is less than or equal to n and be Rm.…

A: Given: We are given a matrix A of size m×n with rank m where m≤n, a vector b of length m×1, and a…

Q: Describe the set {TER²: doo (r,(0, 0)) = 1}.

A: To Describe: the set {x∈ℝ2: d∞(x,(0,0))=1}.

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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