hw1_solu - Solutions for Selected problems of Homework 1 A....

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Unformatted text preview: Solutions for Selected problems of Homework 1 A. Agarwal 1016-331 Linear Algebra-1 Spring 2009-10 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.

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hw1_solu - Solutions for Selected problems of Homework 1 A....

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