4.3 - MATH1850U/2050U: Chapter 4 cont. 1 GENERAL VECTOR...

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MATH1850U/2050U: Chapter 4 cont. .. 1 GENERAL VECTOR SPACES cont. .. Linear Independence (4.3; pg. 190) Definition: If  r S v v v , , , 2 1 is a nonempty set of vectors, then the vector equation 0 2 2 1 1 r r k k k v v v has at least one solution, namely 0 , , 0 , 0 2 1 r k k k If this is the only solution, the S is called a linearly independent set. If there are other solutions, then S is called a linearly dependent set. Example: Show that the set of vectors ) 7 , 2 , 6 ( ), 8 , 2 , 5 ( ), 1 , 0 , 1 ( 3 2 1 v v v is linearly dependent. Example: Show that the polynomials given below form a linearly dependent set. Example: Determine whether the vectors given below form a linearly dependent or linearly independent set.
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MATH1850U/2050U: Chapter 4 cont. .. 2 Example: Determine whether the 2 P vectors given below form a linearly dependent or linearly independent set.
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MATH1850U/2050U: Chapter 4 cont. .. 3 Theorem: A set S with two or more vectors is:
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This note was uploaded on 10/12/2011 for the course MATH 1020 taught by Professor Paulatu during the Spring '11 term at UOIT.

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4.3 - MATH1850U/2050U: Chapter 4 cont. 1 GENERAL VECTOR...

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