Lecture 17 - Feb 11

Lecture 17 - Feb 11 - Wednesday February 11 Lecture 17 :...

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

View Full Document Right Arrow Icon
Wednesday February 11 Lecture 17 : Examples on linear independence (Refers to section 4.2) Expectations : 1. Define a linearly independent set. 2. Determine when a subset of R n is linearly independent. 17.1 Theorem Let S = { v 1 , v 2 , …, v k } be a set of k distinct non-zero vectors in R n . If k > n then the set S cannot be linearly independent. Proof: Let A be the matrix whose columns are v 1 , v 2 , …, v k . Then A is an n by k matrix. If k > n then A has more columns then rows and so A RREF must point to at least one free variable in the system A x = 0 . Hence A x = 0 has infinitely many solutions and so has non-trivial solutions. Thus any set with more vectors then the dimension of R n is not linearly independent. Thus if S = { v 1 , v 2 , …, v k } is linearly independent in R n then k n . 17.2 Example Show that the set { e x , x 2 } is linearly independent in the vector space of all real-valued continuous functions on R . This is shown in class.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/10/2010 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

Page1 / 3

Lecture 17 - Feb 11 - Wednesday February 11 Lecture 17 :...

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