MATH106 Lecture 13: 1.7 - Spanning Sets Linear Independence
14 Oct 2018
School
Department
Course
Professor
Document Summary
Last time we proved that if 72 148. Ir then t. vtts. tt turn it tz the r a subspace of. This subspace is se important that we give it is a special name. 5 turn it tz the r is called the subspace spanned by 73 15 z. B is a spanning set for 5 or that is a non zero vector. 7 is a line through the origin the set or spans. It are all spanning sets for as well. What instead we have two vectors vt vt if. I and i t o f then spanit jz t. tottzlo ti tze ir. So spantu. ve span to a line in r x a span114. 1. Note the vector tz in the second example was of vt so it didn"t contribute anything to span i a multiple. We found that span vt vt span i so instead of spanning a plane they only spanned a line.
