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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online