Week6 - ECON 117 Mathematical Economics Spring 2008 Week 6...

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ECON 117 Spring 2008 Mathematical Economics Week 6 3.1 The Rank of a Matrix Def) The rank of matrix , A () ρ A , is the maximum number of rows (or columns) in that are linearly independent. A Theorem) , A the maximum number of linearly independent rows in A the maximum number of linearly independent columns in . = A Page 1 of 14
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ECON 117 Spring 2008 Mathematical Economics Theorem) , () mn × A { } () m i n , ρ A Theorem) () ( ) = AA Def) Null space of Kernel of = A N = . Let be a matrix with order A × , is a vector space that consists of satisfying . i.e., N A x ⋅= Ax 0 { } , n N = ∈⋅ = Ax x A x 0 \ Q) 21 1 11 2 ⎡⎤ = ⎢⎥ ⎣⎦ A Find in the following diagram. N A Page 2 of 14
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ECON 117 Spring 2008 Mathematical Economics Q) Show that is a vector space over field . () N A \ Theorem) Let be a matrix with order A mn × . Then, ρ = A the number of columns in A nullity of A Def) Nullity of the dimension of . = A N A Page 3 of 14
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ECON 117 Spring 2008 Mathematical Economics
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This note was uploaded on 09/15/2008 for the course ECON 324 taught by Professor Kim during the Spring '08 term at HKUST.

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Week6 - ECON 117 Mathematical Economics Spring 2008 Week 6...

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