: List the vertices in R² of the convex region defined by Ax ≤ b and x ≥ 0 where A = 1 1: 3 (A) (2, 3), ( ½, ½ ), (2, 0), (0, 0), (0, 3) (D) (2, 3), ( ½, ½ ), (2, 0), (0, 0), (0, 3) (G) (2, 3), (½, ½ ), (2, 0), (0, 0), (0, 4) Select ✓ and b = 5 (B) (2, 3), (½, 2), (2, 0), (0, 0), (0, 4) (E) (3, 2), (½, ½), (2, 0), (0, 0), (0, 3) (H) (3, 2), (½, ½), (2, 0), (0, 0), (0, 4) (C) (3, 2), (2, 2), (2, 0), (0, 0), (0, 4) (F) (3, 2), (3, 2), (2, 0), (0, 0), (0, 3)

Q: Let Q be the parallelogram in R2 whose vertices are (1, 1), (3, 2), (4, 5), (2, 4). Find the map T…

A: As per the question we first have to find the linear transformation T, whose inverse which will…

Q: Find and sketch the triangular domain of dependence and region of influence of the given PDE at the…

A: Note: We are not given any particular interval to check the region of influence. So, we have taken…

Q: (x + y + z) dA. 3,

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Q: 5. Consider: max{x, =z,} max{ x, = z,} s.t. xeS where U = z,z2 (a) In the nonnegative orthant, are…

A: Given, max x1=z1maxx2=z2s.t. x∈sWhere U∈z1z2 Part(a): The nonnegative orthant, are the contours of U…

Q: Let A = {X € R³ : X and (1, 2, 3), (1, 0, 1) are linearly depedent} Show that A is closed in R³.

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Q: Let X=ℝ2 and define d,:ℝ2×ℝ2→ℝ d2((x1 ,y1),(x2,y)2)) = max{|x1 - x2|,|y1 - y2|}. Draw the…

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Q: Graph the level curves for z = 2x - 3y for z = 0, 1,2 on the same ry plane, and label them.

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Q: Consider a Bézier surface defined by the following control net. C₁,1 = (2,4,-4) C1,2 (1,0,9) C2,2 =…

A: Given : Bezier surface in the problem.   To calculate :  g1 , 1 and g1 , 0

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A: Given: The given set ,

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Q: Find the extreme points and directions of the following polyhedral sets. а. S = {x:x +2x2 +x3 <10,-x…

A: Hi! As per the norms, we will be answering only the first one. If you need an answer to others then…

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A: Given:Let f:R3→R be defined as: ∀x = (x1, x2, x3)  ∈ R3  f(x1, x2, x3) = 7(x1- x2)2 + 3(1 –x2 )2 +6…

Q: 1. What can you say of a linear maping from P4 (R) to R4 such that the Null space is a line?

A: Let T:V to W be a linear transformation,  then  Null space ={ x in V : T(x)=0 } .

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Q: Exercise III.2. Graph the following sets S in R² and determine which are convex: (i) B = : { ( ₁ ) :…

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Q: Two particles A and B move randomly, at times t = 1,2,... on the set M = {1,...,m}, m≥ 3, reflecting…

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Q: 2. - For each map below, either prove that it is linear or demonstrate that it is not linear. (a) T…

A: Consider a map T:U→V is linear if    (i) T(u+v) =T(u)+T(v)   (ii) T(αu )   = αT(u)   , for all u,v…

Q: 5. Consider the trapezoid D given by the vertices (0,0), (2,0), (1, 1) and (0, 1). (a) Sketch D. (b)…

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Q: E List the vertices in R of the convex region defined by Ax<b and x 2 0 where 1 1 A = 1 and b = 8. 1…

A: This is a problem of LPP.

Q: (3,-4,-2) Show that 323 f dx + gdy + hdz = f(-3) 12x²y^z²dx + 16y³x³z²dy + 8zy r³dz is independent…

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Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: 1.2.1. Find the union C₁ UC2 and the intersection C₁ C₂ of the two sets C₁ and C2, where (a) C₁ =…

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Q: Let E be the solid parallekepiped with vertices Co,0,o).(LLO).co,l,3),(1,0,). C1,2,3),Cし,4).(2,1,1)…

A: Here, vertices are given in 3D. So, for taking limits of X and Y, we'll look for the projection of…

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Q: F . dr, (c) Let f(x, y, z) = x³ + 2yª + 325 and F consists of three line segments from (1,0, 0) to…

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Q: Q. Let (X, B(R), µ) be a Borel measure space. If AnB = 0, B nC = ¢, µ(AnC) = 1,then µ(AUBUC) = 1.…

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Q: For the s,t-network with capacities and flows as shown below. What is the value of the s,t-cut A(X,…

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Q: If F(x, y, z) = (sin x + 2) i+2xz j+ (e-x) k and the path C is the line segment from A(1,2, 1) to…

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Q: The Vertex and the value of p'of the given parabola (x – 4)2 = 12(y – 7) are | - Vertex = (-4, –7);…

A: Use vertex form of parabola

Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

A: We will first try to minimise (xn + yn)/2 using Lagrange multipliers then show that its minimum…