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Unformatted text preview: Solutions for Selected problems of Homework 1 A. Agarwal 1016331 Linear Algebra1 Spring 200910 1. Q22,P.14 Here is an algebraic way of finding w as a linear combination of u and v . Linear combination means, we have to find scalars c 1 ,c 2 such that w = c 1 u + c 2 v . The vector equation will look like " 2 9 # = c 1 " 2 3 # + c 2 " 2 1 # This gives us " 2 9 # = " 2 c 1 + 2 c 2 3 c 1 + c 2 # Solving the system of equations will give us c 1 = 2 ,c 2 = 3. 2. Q56(a),P.27 We will use the fact that  a  2 = a a  u + v  2 +  u v  2 = ( u + v ) ( u + v ) + ( u v ) ( u v ) = ( u u + u v + v u + v v ) + ( u u u v v u + v v ) using the commutative property of the dot product = (  u  2 + 2 u v +  v  2 ) + (  u  2 2 u v +  v  2 ) = 2(  u  2 +  v  2 ) 3. Q60,P.27 Use the fact  u + v  2 =  u  2 + 2 u v +  v  2 that we established in the previous problem to get  u + v  = 3....
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This note was uploaded on 05/11/2010 for the course MTH 1016.331 taught by Professor Dr.anuragagarwal during the Spring '10 term at RIT.
 Spring '10
 Dr.AnuragAgarwal
 Linear Algebra, Algebra, Scalar

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