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
Unformatted text preview: with reasoning based on theorems, denitions, or counterexamples. a) If ~v 1 is a vector in R n , then the set { ~v 1 } is linearly independent. b) If { ~v 1 ,...,~v k } is a linearly dependent set in R n , then { ~v 1 ,...,~v k1 } is linearly dependent. c) If { ~v 1 ,~v 2 } is a linearly independent set in R n , then { ~v 1 ,~v 1~v 2 } is linearly independent. * 5. Let ~x = a b , ~ y = c d , and ~ z = e f be any three vectors in R 2 . a) Prove that { ~x,~ y } is linearly independent if and only if adbc 6 = 0. b) Prove that { ~x,~ y,~ z } is linearly dependent. * Indicates a challenging problem....
View
Full
Document
This note was uploaded on 03/03/2011 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.
 Spring '08
 All
 Linear Algebra, Algebra, Vectors, Sets

Click to edit the document details