MATH136 Lecture Notes - Lecture 20: Free Variables And Bound Variables, Spain, Linear Combination

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

Document Summary

Wednesday, february 26 lecture 20: linear independence. Concepts: linearly independent set, recognize that subsets of linearly independent sets are linearly independent, characterize a linearly independent set as one being a set where no vector is a linear combination of the others. 20. 1 definition generalization of the definition of linear independence. Let v1, v2, , vk be k vectors in a vector space v. the vectors v1, v2, , vk are said to be linearly independent if and only if the only way that. 1v1 + 2v2 + + kvk = 0 can hold true is if 1, 2, , k are all zeroes. 20. 1. 1 example we know that the two functions ex and sin x are vectors in the set f described above. Then s = span{ex, sin x} = { ex + sin x : , belong to } is a subspace of f. show that the set {ex, sin x} is linearly independent.