Math Eco Assignment 1 A172.docx - A172 Question One a In order to fulfilled the condition to solve the problem the number of unknown must be equal to

# Math Eco Assignment 1 A172.docx - A172 Question One a In...

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A172 Question One a) In order to fulfilled the condition to solve the problem, the number of unknown must be equal to the number of equation. In this case, there are 3 unknowns but there’s 6 equations. b) To solve this problem, we can reduce the number of unknown and equation by combining two equation in which Q 1 d = Q 1 s = Q 1 ,Q 2 d = Q 2 s = Q 2 ,Q 3 d = Q 3 s = Q 3 c) Q 1 = 23 5 P 1 + P 2 + P 3 =− 8 + 6 P 1 Q 1 = 31 11 P 1 + P 2 + P 3 11 P 1 + P 2 + P 3 =− 31 Q 2 = 15 + P 1 3 P 2 + 2 P 3 =− 11 + 3 P 2 Q 2 = 26 + P 1 6 P 2 + 2 P 3 P 1 6 P 2 + 2 P 3 =− 26 Q 3 = 19 + P 1 + 2 P 2 4 P 3 =− 5 + 3 P 3 Q 3 = 24 + P 1 + 2 P 2 7 P 3 P 1 + 2 P 2 7 P 3 =− 24 [ 11 1 1 1 6 2 1 2 7 ] [ P 1 P 2 P 3 ] = [ 31 26 24 ] d) | A | =− 11 [ ( 6 ) ( 7 ) ( 2 ) ( 2 ) ] ( 1 ) [ ( 1 ) ( 7 ) ( 2 ) ( 1 ) ] +( 1 )[ ( 1 ) ( 2 ) ( 6 ) ( 1 ) ] | A | =− 401 Ad joint A = C T C = [ 38 9 8 9 76 23 8 23 65 ] T C T = [ 38 9 8 9 76 23 8 23 65 ] Vector P [ P 1 P 2 P 3 ] = 1 401 [ 38 9 8 9 76 23 8 23 65 ][ 31 26 24 ]

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[ P 1 P 2 P 3 ] = 1 401 [ 38 (− 31 ) + 9 (− 26 ) + 8 (− 24 ) 9 (− 31 ) + 76 (− 26 ) + 23 (− 24 ) 8 (− 31 ) + 23 (− 26 ) + 65 (− 24 ) ] [ P 1 P 2 P 3 ] = 1 401 [ 1604
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