math125-lecture 4.1

math125-lecture 4.1 - A vector is an ordered n-tuple of...

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Unformatted text preview: A vector is an ordered n-tuple of numbers ( u 1 , u 2 , ..., u n ) ("pair " n = 2, or "triple" n = 3, or "quadruple", etc.) Sec 4.1 Saturday, February 06, 2010 11:10 PM Section4dot1 Page 1 A vector is an ordered n-tuple of numbers ( u 1 , u 2 , ..., u n ) ("pair " n = 2, or "triple" n = 3, or "quadruple" n = 4, etc.) New notation: u = ( u 1 , u 2 , ..., u n ) (in books, including ours: bold-faced letters are used instead of : u = ( u 1 , u 2 , ..., u n ) 4.1.1 Saturday, February 06, 2010 11:10 PM Section4dot1 Page 2 A vector is an ordered n-tuple of numbers ( u 1 , u 2 , ..., u n ) ("pair " n = 2, or "triple" n = 3, or "quadruple" n = 4, etc.) New notation: u = ( u 1 , u 2 , ..., u n ) (in books, including ours: bold-faced letters are used instead of : u = ( u 1 , u 2 , ..., u n ) Geometrically, a vector represents a direction and a size. "What direction do I go in and how far do I go from where I am now" EX: u = (2, 3) represents 2 across and 3 up "from where I am at now" 4.1.2 Saturday, February 06, 2010 11:10 PM Section4dot1 Page 3 A vector is an ordered n-tuple of numbers ( u 1 , u 2 , ..., u n ) ("pair " n = 2, or "triple" n = 3, or "quadruple" n = 4, etc.) New notation: u = ( u 1 , u 2 , ..., u n ) (in books, including ours: bold-faced letters are used instead of : u = ( u 1 , u 2 , ..., u n ) Geometrically, a vector represents a direction and a size. "What direction do I go in and how far do I go from where I am now" EX: u = (2, 3) represents 2 across and 3 up "from where I am at now" u u u u All of these are u . Without more information, a vector does not say anything about "where" it lies in space 4.1.3 Saturday, February 06, 2010 11:10 PM Section4dot1 Page 4 A vector is an ordered n-tuple of numbers ( u 1 , u 2 , ..., u n ) ("pair " n = 2, or "triple" n = 3, or "quadruple" n = 4, etc.) New notation: u = ( u 1 , u 2 , ..., u n ) (in books, including ours: bold-faced letters are used instead of : u = ( u 1 , u 2 , ..., u n ) Geometrically, a vector represents a direction and a size. "What direction do I go in and how far do I go from where I am now" EX: u = (2, 3) represents 2 across and 3 up "from where I am at now" u u u u All of these are u . Without more information, a vector does not say anything about "where" it lies in space Recall that a single column ( m x 1 ) matrix is an ordered collection of m numbers. We can think of such matrices as vectors 4.1.4 Saturday, February 06, 2010 11:10 PM Section4dot1 Page 5 k + m = ( -3, 2, 3 ) + ( 4, -4, 2 ) = ( -3 + 4, 2 + (-4), 3 + 2 ) = ( 1, -2, 5 ) 4.1.5 Saturday, February 06, 2010 11:30 PM Section4dot1 Page 6 k + m = ( -3, 2, 3 ) + ( 4, -4, 2 ) = ( -3 + 4, 2 + (-4), 3 + 2 ) = ( 1, -2, 5 ) u + v = ( 2, 3 ) + ( 4, 1 ) = ( 2 + 4, 3 + 1 ) = ( 6, 4 ) u v u + v 4.1.6 Saturday, February 06, 2010 11:30 PM Section4dot1 Page 7 k + m = ( -3, 2, 3 ) + ( 4, -4, 2 ) = ( -3 + 4, 2 + (-4), 3 + 2 ) = ( 1, -2, 5 )...
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math125-lecture 4.1 - A vector is an ordered n-tuple of...

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