homework set 12-Solutions

# homework set 12-Solutions - B ˙ ILKENT UNIVERSITY...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: B ˙ ILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set 1 # 12 U. Mu˘gan July 2, 2008 Homework problems from the 2 nd Edition, SECTION 4.2 3 (3) ) 2 A typical vector in W is of the form ~x = ( x 1 , 1 ,x 3 ). Since scalar multiple c~x = ( cx 1 ,c,cx 3 ) is not in W unless c = 1. Hence W is not closed under multiplication by scalar, and therefore W is not a subspace of R 3 . 7 (7) ) Note that the vectors ~x = (1 , 1) and ~ y = (1 ,- 1) are in W . But their sum ~x + ~ y = (2 , 0) is not in W , because | 2 | 6 = | | . Hence, W is not a subspace of R 2 . 8 (8) ) Since x 2 1 + x 2 2 = 0, W is simply the zero subspace { ~ } of R 2 . 10 (10) ) The vectors ~x = (1 , 0) and ~ y = (0 , 1) are in W . But their sum ~x + ~ y = (1 , 1) is not in W , because | 1 | + | 1 | = 2 6 = 1 . Hence, W is not a subspace of R 2 . 11 (11) ) Let ~x = ( x 1 ,x 2 ,x 3 ,x 4 ) and ~ y = ( y 1 ,y 2 ,y 3 ,y 4 ) be the vectors in W , so x 1 + x 2 = x...
View Full Document

## This note was uploaded on 06/18/2010 for the course COMPUTER S Math 225 taught by Professor Yosumhoca during the Spring '10 term at Bilkent University.

### Page1 / 2

homework set 12-Solutions - B ˙ ILKENT UNIVERSITY...

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

View Full Document
Ask a homework question - tutors are online