Notes-Chapter 4-Part 2

Notes-Chapter 4-Part 2 - LINEAR MODELS AND MATRIX ALGEBRA...

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LINEAR MODELS AND MATRIX ALGEBRA - Part 2 Chapter 4 Alpha Chiang, Fundamental Methods of Mathematical Economics 3 rd edition
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Vector Operations Multiplication of vectors An m x 1 column vector u, and a 1 x n row vector v’, yield a product uv’ of dimension m x n. On the other hand, a 1 x n row vector u’ and an n x 1 column vector v, the product u’v will be of dimension 1 x 1. Example 1- 2x1, 1x3, 2x3. [ ] 3 ' 1 4 5 2 3(1) 3(4) 3(5) 3 12 15 ' 2(1) 2(4) 2(5) 2 8 10 u v uv   = =     = =
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Vector Operations Example 2. 1x2, 2x1, 1x1 As written, u’v is a matrix, despite the fact that only a single element is present. 1 x 1 matrices behave exactly like scalars with respect to addition and multiplication: [4] + [8] =[12], [3][7]=[21] a scalar product [ ] [ ] [ ] 9 3 4 7 ' 3(9) 4(7) 55 - a scalar u v u v   = =     = + =
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Vector Operations Example 3. - Given a row vector u’ = [3
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This note was uploaded on 11/09/2011 for the course ECON 101 taught by Professor Richards during the Spring '11 term at Cambrian College.

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Notes-Chapter 4-Part 2 - LINEAR MODELS AND MATRIX ALGEBRA...

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