20E_sheet1 - FACT SHEET FOR 20E EXAM 1 1. From Chapter 1...

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Unformatted text preview: FACT SHEET FOR 20E EXAM 1 1. From Chapter 1 Dot product of two vectors v = ( v 1 , v 2 , . . . , v n ) and w = ( w 1 , w 2 , . . . , w n ): v w = v 1 w 1 + v 2 w 2 + . . . + v n w n . Cross produce of two vectors in 3D (its a vector!): v w = ( v 2 w 3- v 3 w 2 , v 3 w 1- v 1 w 3 , v 1 w 2- v 2 w 1 ) . We have that v ( v w ) = w ( v w ) = 0 and the length v w is the area of the parallelogram spanned by v and w . The direction obeys the right hand rule. The equation for a line through the vector x and in the direction v is ( t ) = x + t v . The matrix product of an n m matrix ( a ij ) and an m k matrix ( b ij ) is the n k matrix ( c ij ) with c ij = m l =1 a il b lj . The determinant of a 2 2 matrix ( a ij ) is | A | = a 11 a 22- a 12 a 21 . This is the area of the parallelogram spanned by the vectors ( a 11 , a 12 ) and ( a 21 , a 22 )....
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This note was uploaded on 03/16/2010 for the course MATH 223B taught by Professor Staff during the Spring '09 term at University of Arizona- Tucson.

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20E_sheet1 - FACT SHEET FOR 20E EXAM 1 1. From Chapter 1...

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