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Question 4: [10pt total] Let ū = (1,4), T = (–7,5), and W = (-2, -1)....
Question 4: [10pt total] Let 7 = (1,4), 7 = (-7,5), and =(-2,-1). Calculate the following: Q4)a) [2pt] 7+7= Q4)b) (2pt] 37 Q4)c) [2pt] 27 - 7+3= Q4)d) (3pt](-1,-1,2) + (7,0,-5) - (2,8,0) = Q4)e) [3pt] (2a + 2b,b,c-a) -2(a, a +b,c) =
Question 1: [10pt total] Consider the line through the points (-3,-4) and (1,4). Q1)a) (3pt) Graph the line on the ey-plane below: 6 4 2 6 4 2 0 2 4 6 2 Q1)b) (3pt] Calculate the equation of the line in the form y=mx+b. Equation of the line: Q1)c) (4pt] Calculate a parametrization of the line. Parametrization of the line:
Question 6: (10pt total] Q6)a) (5pt] Apply a (3,2)-linear-distortion to the following square and sketch the result on the same coordinate axis. 6 4 2 -6 2 0 2 2 -4 -6 Q6)b)i) [2pt] Calculate the area of the original square: Q6)b)ii) [3pt] Calculate the area of the you drew in Q6)a):
5 3 1 Let ū = < 2,-3> V = <-2,0 > w = <3,3 > Graph vectors ū, ū, and w in standard position with corresponding terminal points, A, B, and C, respectively. (72 point) What is the length of the altitude of AABC from vertex A? (72 point) -5 -3 -1 -1 0 1 3 5 -3 -5
1-4 Player 2 2 Question 4: (15pt total] Consider the following game: X Y Player 1 p A1, 32, 4 1-p B 0,28,0 Suppose Player 1 plays A with probability p, and Player 2 plays X with probability q. Let E1 (-) and E2(-) be the expected payoff functions. 4)a) [8pt total] Calculate the following: 4)a)i) (2pt] E1(A) 4)a) ii) (2pt] E1(B) 4)a) iii) [2pt] E2(X) = 4)a)iv) (2pt] E(Y) = 4)b) (3pt) Indifference strategy for Player 1: Answer: 4)c)...
Let ū = [1,-1, 1], v = (-2,-1, 3] and W = (-1, 2, 2). Find (u x D) • w O Does not exist 7 -14 10
Player 2 9 1-9 Question 4: (15pt total] Consider the following game: X Y Player 1 P A 1,3 2,4 1-PB 0,2 8,0 Suppose Player 1 plays A with probability p, and Player 2 plays X with probability q. Let E (-) and E2(-) be the expected payoff functions. 4)a) [8pt total] Calculate the following: 4)a)i) (2pt] E(A) = 4)a)ii) [2pt] E (B) = 4)a)iii) [2pt] E(X) = 4)a)iv) [2pt] E2(Y) = 4)b) (3pt] Indifference strategy for Player 1: Answer:...
Question 7: [10pt total] Consider the following voter profile: Votes 13 9 8 10 Preferences А с B D B с D A с B D А D B с Calculate the following: 7)a) [3pt) Social ranking under the Plurality system. Plurality Social Ranking: 7)b) (3pt) Social ranking under the Instant Runoff system. Instant Runoff Social Ranking: 7)c) [4pt Condorcet winner (if one exists). Condorcet Winner:
1. Let {ü, 7,w, i}, where u = (3,-2), v = (0,4), ū = (-1,5) and i = (-6,4). Find the components of the resultants obtained by doing the following linear combinations. a. r = 2ū - 40 b. š= 3ū – +20 +
problem 1 and problem 2 please , thankyou very
much
PROBLEM 1 (25%) Find: Let: ū= (1,-1,-2) v = (-2,-2,3) w = (3,-1,1) (a) The angle between ū and w (b) Orthogonal projection of u against v (c) The area of parallelogram formed by u dan v (d) The volume of parallelpiped shaped byū, v, dan w PROBLEM 2 (15%) Determine if these sets of points are coplanar: (a) A(1,1,-3); B(0,1,-2); C(-3, 1, 1); D(2, 1, -4) (b) E(1,1,-1); F(0,1,1);...