# HW01 - EE 203000 Linear Algebra Homework#1(Due October 9...

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Unformatted text preview: EE 203000 Linear Algebra Homework #1 (Due October 9, 2009 BEFORE class) Note: Detailed derivations are required to obtain a full score for each problem. (Total 100%) 1. (6%) Prove Theorem 1.2 (c). 2. (6%+6%) Let u1D449 = { ( u1D44E 1 ,u1D44E 2 ) : u1D44E 1 ,u1D44E 2 ∈ ℝ } . Determine whether or not u1D449 is a vector space over ℝ under the operations of addition and scalar multiplication defined below. (If it is true, show your reasons. If not, specify all the conditions that fail.) (i) For ( u1D44E 1 ,u1D44E 2 ), ( u1D44F 1 ,u1D44F 2 ) ∈ u1D449 and u1D450 ∈ ℝ , define ( u1D44E 1 ,u1D44E 2 ) + ( u1D44F 1 ,u1D44F 2 ) = ( u1D44E 1 + u1D44F 1 , − u1D44E 2 − u1D44F 2 ) and u1D450 ( u1D44E 1 ,u1D44E 2 ) = ( u1D450u1D44E 1 ,u1D44E 2 ) . (ii) For ( u1D44E 1 ,u1D44E 2 ), ( u1D44F 1 ,u1D44F 2 ) ∈ u1D449 and u1D450 ∈ ℝ , define ( u1D44E 1 ,u1D44E 2 ) + ( u1D44F 1 ,u1D44F 2 ) = ( u1D44E 1 + u1D44F 1 + 1 ,u1D44E 2 + u1D44F 2 + 1) and u1D450 ( u1D44E 1 ,u1D44E 2 ) = ( u1D450u1D44E...
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## This note was uploaded on 11/09/2011 for the course EE EE taught by Professor Ee during the Spring '11 term at National Chiao Tung University.

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HW01 - EE 203000 Linear Algebra Homework#1(Due October 9...

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