MATH136 Lecture Notes - Lecture 3: Hyperplane, Linear Combination

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

Document Summary

Wednesday, may 10 lecture 5 : basis of subspaces of n (refers to section 1. 2: basis of a subspace, standard basis of n, finding a basis by removing redundant vectors, plane, hyperplane, k-flat. We restate formally the definition of a concept introduced at the end of the lecture 3. 5. 1 definition if s = span{v1, v2, , vk} where {v1, v2, , vk} is a linearly independent subset of vectors in n then we say that {v1, v2, , vk} is a basis of the subspace s. 5. 1. 1 example we saw that the set b = {e1, e2, e3, , en} spans n. We easily verify in class that this set is linearly independent. Then by definition b forms a basis of n (when viewed as a subset of n) . The set is called the standard basis of n. 5. 1. 2 example the set {(1, 2, 3)} is basis of the subspace s = span{(1, 2, 3)}.