lecture6 - Mathematical Economics Lecture 6 Yu Ren WISE...

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Mathematical Economics: Lecture 6 Yu Ren WISE, Xiamen University October 10, 2012
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math Chapter 11 Linear Independence Outline 1 Chapter 11 Linear Independence Yu Ren Mathematical Economics: Lecture 6
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math Chapter 11 Linear Independence New Section Chapter 11: Linear Independence Yu Ren Mathematical Economics: Lecture 6
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math Chapter 11 Linear Independence Linear Independence Vector V 1 , · · · , V k in R n are linear dependent if and only if c 1 , · · · , c k not all zero, s.t. c 1 V 1 + · · · + c k V k = 0. Yu Ren Mathematical Economics: Lecture 6
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math Chapter 11 Linear Independence Linear Independence Vector V 1 , · · · , V k in R n are linear independent if and only if c 1 V 1 + · · · + c k V k = 0 implies c 1 = c 2 = · · · = c k = 0 Yu Ren Mathematical Economics: Lecture 6
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math Chapter 11 Linear Independence Linear Independence; Example Example 11.2 The vectors w 1 = 1 2 3 , w 2 = 4 5 6 , and w 3 = 7 8 9 are linearly dependent in R 3 , since 1 · 1 2 3 - 2 · 4 5 6 + 1 · 7 8 9 = 0 0 0 as can easily be verified. Yu Ren Mathematical Economics: Lecture 6
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math Chapter 11 Linear Independence Linear Independence Theorem 11.1 : Vectors v 1 , · · · , v k in R n are linearly dependent if and only if the linear system A = ( v 1 , · · · , v k ) , Ac = 0 has nonzero solution ( c 1 , · · · , c k ) . Yu Ren Mathematical Economics: Lecture 6
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math Chapter 11 Linear Independence Linear Independence Theorem 11.2 : A set of n vectors v 1 , · · · , v n in R n is linearly independent if and only if det ( v 1 , · · · , v n ) 6 = 0 Yu Ren Mathematical Economics: Lecture 6
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