![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](http://img.homeworklib.com/questions/7f6c46a0-0aec-11eb-845a-f351f280426d.png?x-oss-process=image/resize,w_560)
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Question 4: [10pt total] Let 7 = (1,4), 7 = (-7,5), and =(-2,-1). Calculate the following:...
Question 4: [10pt total] Let ū = (1,4), T = (–7,5), and W = (-2, -1)....
Question 4: [10pt total] Let ū = (1,4), T = (–7,5), and W = (-2, -1). Calculate the following: Q4)a) [2pt] 7 + V Q4)b) [2pt] 3 V Q4)c) [2pt] 27 – +3W 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...
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:
1-4 Player 2 2 Question 4: (15pt total] Consider the following game: X Y Player 1...
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)...
Player 2 9 1-9 Question 4: (15pt total] Consider the following game: X Y Player 1...
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 6: (10pt total] Q6)a) (5pt] Apply a (3,2)-linear-distortion to the following square and sketch the...
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):
Question 7: [10pt total] Consider the following voter profile: Votes 13 9 8 10 Preferences А...
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:
Question 8: [10pt total] Consider the following voter profile: Votes 4 12 3 B с D...
Question 8: [10pt total] Consider the following voter profile: Votes 4 12 3 B с D Preferences D C А B D B Assume the voting system is the Borda voting system. 8)a) [3pt) Calculate the social ranking, assuming the voters voted sincerely? Social Ranking: 8)b) [6pt) Show that there is a way for D to win the election through tactical voting, and calculate the new social ranking. New Social Ranking: 8)c) [1pt] What is the type of tactical voting...
These are linear algebra problems. 1 4 1 1 2 7 2 2 Let A 1 4 .. 1 2 find Its Inverse. Decide whether the matrix A is in...
These are linear algebra problems.
1 4 1 1 2 7 2 2 Let A 1 4 .. 1 2 find Its Inverse. Decide whether the matrix A is invertible, and if so, use the adjoint method Enter as a matrix, exactly in fractional from if required, if not invertible enter "NA" A-1 la b -2a -2b -2c d e f d = -2,find Given that g hi g-3d h-3e -3f -2a -2b -2c d f g 3d h 3e...
Question 5: [10pt total] Let G be the following graph: True for False: Which of the...
Question 5: [10pt total] Let G be the following graph: True for False: Which of the following statements are true about G? 5)a) (1pt] G is a directed graph: 5)f) [1pt] G is bipartite: 5)b) [1pt] G is a weighted graph: 5)g) (1pt] G has a leaf vertex: ......... 5)c) [1pt] G is a multi-graph: 5)h) [1pt] G is planar: 5)d) [1pt] G is a loop graph: 5)i) [1pt] G is Eulerian: 5)) (1pt] G is a complete graph: 5)j)...
4, =(7,5), u =(-3,-1) 2) Let v = (1,-5), v = (-2,2) and let L be...
4, =(7,5), u =(-3,-1) 2) Let v = (1,-5), v = (-2,2) and let L be a linear operator on Rwhose matrix representation with respect to the ordered basis {u,,,) is A (3 -1 a) Determine the transition matrix (change of basis matrix) from {v, V, } to {u}. (Draw the commutative triangle). b) Find the matrix representation B, of L with respect to {v} by USING the similarity relation
Question 4: [10pt total] Let ū = (1,4), T = (–7,5), and W = (-2, -1). Calculate the following: Q4)a) [2pt] 7 + V Q4)b) [2pt] 3 V Q4)c) [2pt] 27 – +3W 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:
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)...
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 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):
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:
Question 8: [10pt total] Consider the following voter profile: Votes 4 12 3 B с D Preferences D C А B D B Assume the voting system is the Borda voting system. 8)a) [3pt) Calculate the social ranking, assuming the voters voted sincerely? Social Ranking: 8)b) [6pt) Show that there is a way for D to win the election through tactical voting, and calculate the new social ranking. New Social Ranking: 8)c) [1pt] What is the type of tactical voting...
These are linear algebra problems.
1 4 1 1 2 7 2 2 Let A 1 4 .. 1 2 find Its Inverse. Decide whether the matrix A is invertible, and if so, use the adjoint method Enter as a matrix, exactly in fractional from if required, if not invertible enter "NA" A-1 la b -2a -2b -2c d e f d = -2,find Given that g hi g-3d h-3e -3f -2a -2b -2c d f g 3d h 3e...
Question 5: [10pt total] Let G be the following graph: True for False: Which of the following statements are true about G? 5)a) (1pt] G is a directed graph: 5)f) [1pt] G is bipartite: 5)b) [1pt] G is a weighted graph: 5)g) (1pt] G has a leaf vertex: ......... 5)c) [1pt] G is a multi-graph: 5)h) [1pt] G is planar: 5)d) [1pt] G is a loop graph: 5)i) [1pt] G is Eulerian: 5)) (1pt] G is a complete graph: 5)j)...
4, =(7,5), u =(-3,-1) 2) Let v = (1,-5), v = (-2,2) and let L be a linear operator on Rwhose matrix representation with respect to the ordered basis {u,,,) is A (3 -1 a) Determine the transition matrix (change of basis matrix) from {v, V, } to {u}. (Draw the commutative triangle). b) Find the matrix representation B, of L with respect to {v} by USING the similarity relation
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