MATH 330 H45

MATH 330 H45 - Math 330 Homework 4.5 (Pages 261,262) (6)...

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: Math 330 Homework 4.5 (Pages 261,262) (6) Find a basis and state the dimension of the following: 3 a + 6 b- c 6 a- 2 b- 2 c- 9 a + 5 b + 3 c- 3 a + b + c : a, b, c R SOLUTION: 3 a + 6 b- c 6 a- 2 b- 2 c- 9 a + 5 b + 3 c- 3 a + b + c = a 3 6- 9- 3 + b 6- 2 5 1 c - 1- 2 3 1 Shows that the three indicated column vectors have a span which produces the subspace. However, unless these three vectors are linearly independent, they do not form a basis: 3 6- 1 6- 2- 2- 9 5 3- 3 1 1 ( R 2 ,R 3 ,R 4) ( R 2- 2 R 1 ,R 3+3 R 1 ,R 4+ R 1) = 3 6- 1- 14 23 7 This shows we do not have three pivots so the vectors are dependent. However, since the first two vectors are not multiples of each other they are independent and hence our space has dimension 2 with basis 3 6- 9- 3 , 6- 2 5 1 (8) Find a basis and state the dimension of...
View Full Document

This note was uploaded on 09/19/2009 for the course MATH 330 taught by Professor Johnson,j during the Spring '08 term at Nevada.

Page1 / 3

MATH 330 H45 - Math 330 Homework 4.5 (Pages 261,262) (6)...

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