MATH115 Lecture 7: lect115_7_f14

• School: University of Waterloo
• Department: Mathematics
• Course: MATH115
• Professor: Tina Davidson

Document Summary

Friday, september 19 lecture 7 : basis of n. 7. 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. 7. 1. 1 example we saw that the set {e1, e2, e3, , en} spans n. N (when viewed as a subspace of n) . The set is called the standard basis of n. this set is linearly independent. Then, by definition, {e1, e2, e3, , en} forms a basis of. 7. 1. 2 example the set {(1, 2, 3)} is basis of the subspace s = span{(1, 2, 3)}. The set s is a line which contains the vector (0, 0, 0). Note that a set can have more than one basis. For example {(2, 4, 6)} is also basis for the subspace s = span{(1, 2, 3)}.