s08week05a - Math 205 Spring 2008 B Dodson Week 5a(first...

Info iconThis preview shows pages 1–3. 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 205, Spring 2008 B. Dodson Week 5a: (first part) 2.2 Subspaces/Spanning (continued) 2.3 Independence/Bases ———– Linear Independence/Bases and Dimension Vectors v 1 , v 2 , . . . , v k in a vector space V are linearly dependent if there are scalars c 1 , c 2 , . . . , c k so 0 = c 1 v 1 + c 2 v 2 + ··· + c k v k , with at least one c j = 0 . Such a vector equation is said to be a relation of linear dependence among the v 1 , v 2 , . . . , v k . A collection of vectors for which the only solution of the vector equation is the trivial solution, c 1 = 0 , . . . , c k = 0 is said to be linearly independent. Examples: (1) i, j in R 2 ; and (2) { i, j, k } in R 3 ; are linearly independent. Verification: c 1 i + c 2 j + c 3 k = c 1 (1 , , 0) + c 2 (0 , 1 , 0) + c 3 (0 , , 1) = ( c 1 , c 2 , c 3 ) = (0 , , 0) = 0 , only when c 1 = 0 , c 2 = 0 , c 3 = 0 . 2 Our main objective is the definition of basis....
View Full Document

This note was uploaded on 02/29/2008 for the course MATH 205 taught by Professor Zhang during the Spring '08 term at Lehigh University .

Page1 / 5

s08week05a - Math 205 Spring 2008 B Dodson Week 5a(first...

This preview shows document pages 1 - 3. Sign up to view the full document.

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