Definitions for Exam 1 - Definitions 2.3 • If S = {v1,...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Definitions 2.3 If S = { v 1 , v 2 , …, v k } is a set of vectors in R n , then the set of all linear combinations of v 1 , v 2 , …, v k is called the span of v 1 , v 2 , …, v k and is denoted by span( v 1 , v 2 , …, v k ) or span(S). If span(S) = R n , then S is called a spanning set for R n . A set of vectors v 1 , v 2 , …, v k is linearly dependent if there are scalars c 1 , c 2 , …, c k , at least one of which is not zero, such that: c 1 v 1 +c 2 v 2 + +c k v k = 0 . A set of vectors that is not linearly dependent is called linearly independent . 2.2 A system of linear equations is called homogeneous if the constant term in each equation is zero. A matrix is in reduced row echelon form if it satisfies the following properties. 1. It is in row echelon form. 2. The leading entry in each nonzero row is a 1 (called a leading 1 ). 3. Each column containing a leading 1 has zeros everywhere else. The
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/13/2008 for the course MATH 215 taught by Professor Yeap during the Spring '08 term at University of Arizona- Tucson.

Ask a homework question - tutors are online