math125-lecture 4.2rev - (recall) Let v 1 , v 2 , . . . , v...

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Unformatted text preview: (recall) Let v 1 , v 2 , . . . , v k be some vectors in R n . A vector v in R n is called a linear combination of v 1 , v 2 , . . . , v k if v = c 1 v 1 + c 2 v 2 + . . . + c k v k for some real numbers (scalars) c 1 , c 2 , . . . , c k Sec 4.2.REV Monday, February 15, 2010 10:15 PM Section4dot2REV Page 1 (recall) Let v 1 , v 2 , . . . , v k be some vectors in R n . A vector v in R n is called a linear combination of v 1 , v 2 , . . . , v k if v = c 1 v 1 + c 2 v 2 + . . . + c k v k for some real numbers (scalars) c 1 , c 2 , . . . , c k Observe that- 2 v 1 + 3 v 2 = - 2 ( 3, 12, - 2 ) + 3 ( 4, - 7, 3 ) = ( - 6, - 24, 4 ) + ( 12, - 21, 9 ) = (6, - 45, 13 ) = v Hence v is a linear combination of v 1 and v 2 4.2.REV.1 Monday, February 15, 2010 10:15 PM Section4dot2REV Page 2 (recall) Let v 1 , v 2 , . . . , v k be some vectors in R n . A vector v in R n is called a linear combination of v 1 , v 2 , . . . , v k if v = c 1 v 1 + c 2 v 2 + . . . + c k v k for some real numbers (scalars) c 1 , c 2 , . . . , c k Observe that- 2 v 1 + 3 v 2 = - 2 ( 3, 12, - 2 ) + 3 ( 4, - 7, 3 ) = ( - 6, - 24, 4 ) + ( 12, - 21, 9 ) = (6, - 45, 13 ) =...
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This note was uploaded on 06/07/2011 for the course MATH 125 taught by Professor Tom during the Fall '07 term at University of Illinois at Urbana–Champaign.

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math125-lecture 4.2rev - (recall) Let v 1 , v 2 , . . . , v...

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