Compilation - PSET1 - JP S PSET NUMBER ONE $Post If MatrixQ...

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JP' S PSET NUMBER ONE $Post : = If @ MatrixQ @ ± D , MatrixForm @ ± D , ± D We define the following matrices : a = K 4 - 1 6 9 O K 4 - 1 6 9 O b = K 0 3 3 - 2 O K 0 3 3 - 2 O c = K 8 3 6 1 O K 8 3 6 1 O d = K 1 2 O K 1 2 O f = K 5 7 O K 5 7 O g = K 1 0 3 2 5 7 O K 1 0 3 2 5 7 O We solve for the following, holding that they are possible. a + b K 4 2 9 7 O b - c K - 8 0 - 3 - 3 O Subtracting matrix c from b H 2. a L H 3. c L K 192.` - 18.` 216.` 54.` O Multiplying a vector to the matrices and their prooduct For the following, we slve for the tranposes : Transpose @ d D .f H 19 L
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Transpose @ f D .d H 19 L Transpose @ f D .f H 74 L Transpose @ d D .d H 5 L a.g K 2 - 5 5 24 45 81 O Product of two matrices Proving that the tranpose of a tranpose of a matrix wil yield the original matrix. Using matrix a, we have : Transpose @ a D h = K 4 6 - 1 9 O K 4 6 - 1 9 O Transpose @ h D K 4 - 1 6 9 O This value is equal to the original matrix a. Proving that the product of tranpose and the tranpose of Transpose @ a.b D K - 3 27 14 0 O Transpose @ a D .Transpose @ b D K 18 0 27 - 21 O NUMBER TWO The summation notation of the given production function : ± p = 1 q = 1 n p.q NUMBER THREE We define the matrices as follows : A = 7 5 1 3 8 6 7 5 1 3 8 6 2 LBYECO2 PSET1.nb
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B = K 4 9 10 2 6 5 O K 4 9 10 2 6 5 O F = 2 6 7 2 6 7 Solve whenever possible : Proving that the Associative law for matrces apply. Using the given matrices, we get : H A.B L .F 1299 357 1506 A. H B.F L 1299 357 1506 Therefore, the grouping of the matrices does not affect the product. NUMBER FOUR Clear @ A, B, F D We define the matrices as : In[1]:= A = K 4 6 3 5 O B = K 2 0 7 3 8 1 O F = 4 1 3 0 1 5 Out[1]= 88 4, 6 < , 8 3, 5 << Out[2]= 88 2, 0, 7 < , 8 3, 8, 1 << Out[3]= 88 4, 1 < , 8 3, 0 < , 8 1, 5 << Solve for the ff, whenever possible : A.B K 26 48 34 21 40 26 O Product of A Transpose @ A D .B K 17 24 31 27 40 47 O LBYECO2 PSET1.nb 3
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In[4]:= B.Transpose @ A D incompatible Dot::dotsh : Tensors 88 2, 0, 7 < , 8 3, 8, 1 << and 88 4, 3
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This note was uploaded on 09/22/2011 for the course ECON 101 taught by Professor Mr.tull during the Spring '11 term at De La Salle University.

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Compilation - PSET1 - JP S PSET NUMBER ONE $Post If MatrixQ...

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