MATH136 Lecture Notes - Lecture 4: Scalar Multiplication, Linear Combination

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Robert Andre

Document Summary

Concepts: subspace of a vector space. , prove that the intersection of two subspaces is a subspace, span of a finite set of vectors is a subspace. Monday, may 8 lecture 4 : subspaces of n (refers to sections 1. 3: lines and planes which are subspaces in 3, determining if a subset is a subspace of n. Up to now we have referred to the elements of the set n as vectors. For reasons which we will make clear later we will now refer to n not simply as the set of all n-tuples of real numbers but as a vector space. For example, rather than say the set 3 we will say the vector space 3. 4. 1 definition we say that a subset w of the vector space n is a subspace of n if w: w is a non-empty subset of n, w is closed under scalar multiplication and closed under addition .