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MATH2107-4-40

# MATH2107-4-40 - Section 4.4 Coordinate Systems Linear...

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Section 4.4 Coordinate Systems Linear Algebra and its Applications David C. Lay — Winter 2008 – p. 1/8

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Given a basis B = { b 1 ,..., b n } for a vector space V . For each x V there exists a unique set of scalars c 1 ,c 2 ,...,c n such that x = c 1 b 1 + c 2 b 2 + · · · + c n b n The scalars c 1 ,c 2 ,...,c n are called the coordinates of x relative to the basis B . These coordinates can be denoted by [ x ] B = c 1 . . . c n — Winter 2008 – p. 2/8
and called the coordinate vector of x relative to B or the B -coorindate vector of x . The mapping V R n x [ x ] B is called the coordinate mapping. — Winter 2008 – p. 3/8

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Graphical Interpretation Suppose e 1 = bracketleftbigg 1 0 bracketrightbigg , e 2 = bracketleftbigg 0 1 bracketrightbigg are the vectors in the basis B for R 2 . — Winter 2008 – p. 4/8
Suppose b 1 = e 1 , b 2 = bracketleftbigg 1 2 bracketrightbigg . Let B 1 = { b 1 , b 2 } . — Winter 2008 – p. 5/8

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Example Let b 1 = bracketleftbigg

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