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Unformatted text preview: Homework 1: Answer Key Econometrics: ECO 721 Fall 2009 1. A = & 1 & 3 & 2 & 1 Â¡ , B = & 1 & 3 2 4 Â¡ : i. ( AB ) = B A = & 7 & 4 9 2 Â¡ ii. AB = & 7 9 & 4 2 Â¡ 6 = BA = & 7 6 & 6 2 Â¡ 2. X = 2 6 6 6 4 1 x 1 z 1 1 x 2 z 2 . . . . . . . . . 1 x N z N 3 7 7 7 5 i. X i =N = 1 N 2 4 1 1 Â¡ Â¡ Â¡ 1 x 1 x 2 Â¡ Â¡ Â¡ x N z 1 z 2 Â¡ Â¡ Â¡ z N 3 5 2 4 1 1 1 3 5 = 1 N 2 4 1 + 1 + Â¡ Â¡ Â¡ + 1 x 1 + x 2 + Â¡ Â¡ Â¡ + x N z 1 + z 2 + Â¡ Â¡ Â¡ + z N 3 5 = 2 4 1 x z 3 5 ii. X X=N = 1 N 2 4 1 1 Â¡ Â¡ Â¡ 1 x 1 x 2 Â¡ Â¡ Â¡ x N z 1 z 2 Â¡ Â¡ Â¡ z N 3 5 2 6 6 6 4 1 x 1 z 1 1 x 2 z 2 . . . . . . . . . 1 x N z N 3 7 7 7 5 = 1 N 2 4 1 + 1 + Â¡ Â¡ Â¡ + 1 x 1 + x 2 + Â¡ Â¡ Â¡ + x N z 1 + z 2 + Â¡ Â¡ Â¡ + z N x 1 + x 2 + Â¡ Â¡ Â¡ + x N x 2 1 + x 2 2 + Â¡ Â¡ Â¡ + x 2 N x 1 z 1 + x 2 z 2 + Â¡ Â¡ Â¡ + x N z N z 1 + z 2 + Â¡ Â¡ Â¡ + z N x 1 z 1 + x 2 z 2 + Â¡ Â¡ Â¡ + x N z N z 2 1 + z 2 2 + Â¡ Â¡ Â¡ + z 2 N 3 5 = 2 4 1 1 N P x i 1 N P z i 1 N P x i 1 N P x 2 i 1 N P x i z i 1 N P z i 1 N P x i z i 1 N P z 2 i 3 5 :...
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