MATH2107-4-31 - Section 4.3 Linearly independent sets bases...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 4.3 Linearly independent sets; bases Linear Algebra and its Applications David C. Lay — Winter 2008 – p. 1/14
Background image of page 1

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

View Full DocumentRight Arrow Icon
Let’s start with a vector space V and an ordered subset { v 1 , ··· , v p } ⊂ V . The ideas are similar to those for R n . { v 1 , ··· , v p } ⊂ V is said to be linearly independent if c 1 v 1 + ··· + c p v p = 0 (1) has only the trivial solution c 1 = ··· = c p . The set { v 1 , ··· , v p } is said to be linearly dependent if (1) has a non-trivial solution. i.e. c i n = 0 for at least one i . When { v 1 , ··· , v p } is linearly dependent there is a linear dependence relation among the vectors v 1 , . . . , v p . — Winter 2008 – p. 2/14
Background image of page 2
Theorem { v 1 , ··· , v p } with v 1 n = 0 is linearly dependent if and only if some v j , j > 1 is a linear combination of the preceeding vectors, v 1 , . . . , v j 1 . — Winter 2008 – p. 3/14
Background image of page 3

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

View Full DocumentRight Arrow Icon
e 1 = 1 0 0 , e 2 = 0 1 0 , e 3 = 0 0 1 . 1. Show
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/26/2010 for the course MATH Math2107 taught by Professor Lanihaque during the Fall '10 term at Carleton.

Page1 / 13

MATH2107-4-31 - Section 4.3 Linearly independent sets bases...

This preview shows document pages 1 - 5. Sign up to view the full document.

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