Matrices. Special Matrices Matrix Addition and Subtraction Example.
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Transcript of Matrices
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MATRICESAPLICACIÓN ECONÓMICA
Y X Y² X² XY
102 114 10404 12996 11628
106 118 11236 13924 12508
108 126 11664 15876 13608
110 130 12100 16900 14300
122 136 14884 18496 16592
124 140 15376 19600 17360
128 148 16384 21904 18944
130 156 16900 24336 20280
142 160 20164 25600 22720
148 164 21904 26896 24272
150 170 22500 28900 25500
154 178 23716 31684 27412
1524 1740 197232 257112 225124
∑Y ∑X ∑ Y² ∑ X² ∑ XY²
DETERMINAR EL MODELO ECONÓMICO PARA LA SIGUIENTE INFORMACIÓN
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1. SE DETERMINA EL MODELO MATRICIAL
Y = X B + e
102 1 114 e1106 1 118 e2108 1 126 e3
110 1 130 e4
122 1 136 B o e5
124 = 1 140 + e6
128 1 148 e7
130 1 156 B1 e8142 1 160 e9148 1 164 e10150 1 170 e11154 1 178 e12
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2. SE CALCULA LA MATRIZ COMPLEMENTARIA X´X
X
1 1141 118
X ´ 1 126X´X
1 130
1 1 1 1 1 1 1 1 1 1 1 1 1 136 12 1740
1 140 =
114 118 126 130 136 140 148 156 160 164 170 178 1 148 174025711
2
1 156
1 1601 1641 1701 178
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3) SE HALLA EL DETERMINATE X´X
X´X = 3085344 - 3027600
X´X = 57744
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4 ) SE CAMBIA A MATRIZ DE COFACTORES O ADJUNTA
257112 -1740
-1740 12
X´X
12 1740
1740 257112
De la matriz complementaria se intercambian los valores extremos y se coloca el signo menos a los valores que son iguales y se obtiene la MATRIZ ADJUNTA
Matriz Complementaria
MATRIZ ADJUNTA
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5 ) SE HALLA LA MATRIZ INVERSA ( X ´ X ) ¯ ¹
257112 -1740
57744 57744 4,45262 -0,03013
=
-1740 12 -0,030130,000207
8
57744 57744
( X ´ X ) ¯ ¹
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6 ) CÁLCULO DEL VECTOR COLUMNA X´Y
Y
102106108
X ´ 110 X´Y122
1 1 1 1 1 1 1 1 1 1 1 1 124 1524 128 =
114 118 126 130 136 140 148 156 160 164 170 178 130 225124142148150154
2X12
12X1
2X1
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7 ) CÁLCULO DE LOS ESTIMADORES B = X´X ¯¹ X´Y
2X2 2X1 2X1
-1
X´X X´Y
4,45262 -0,03013 1524 6785,79 -6783,66 2,13 → Bo
= =
-0,030130,000207
8 225124 -45,9227 46,7839 0,86 → B1
Matriz inversa Vector columna
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8) EL MODELO SERA:
Y = B o + B1 X
Y = 2,13 + 0,86X