MAT 1341 Study Guide - Final Guide: Row Echelon Form, Augmented Matrix, Linear System
13 Dec 2016
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Definition of a span contains zero vector closed under addition closed under scalar multiplication all planes through the origin are subspaces span. The big theorem about spans a. spans are subspaces (proof: apply the subspace test. How to check if two spans are equal test to see if all elements in each span are in the span of the other. Let v be a vector space and be a set of vectors in v. is called a. Theorem relating linearly independent sets to spanning sets basis of v if it is linearly independent and it spans v. Basis and dimension a linearly independent spanning set of v the biggest possible li set in v the smallest possible spanning set in v. Dimension of v, denoted dim(v), is defined as the number of elements in any linearly independent spanning set (any basis) of v.
