Applied Mathematics 1411A/B Chapter 4.5.1: Applied Mathematics 1411A/B Chapter 4.5.: Applied Mathematics 1411A/B Chapter 4.5: Applied Mathematics 1411A/B Chapter 4.: Section 4.5.1

• School: Western University
• Department: Applied Mathematics
• Course: Applied Mathematics 1411A/B
• Professor: Bogdan Tudose

Document Summary

We showed that the standard basis in rn contains n vectors. In r3 there is 3 standard vectors in the basis and in r2 there is 2 vectors etc. We think of space as three-dimensional, a plane as two-dimensional and a line as one dimensional thus there seems to be a link between the number of vectors in a basis and the dimension of a vector space! All bases for a finite-dimensional vector space have the same number of vectors. So, if a vector space is finite dimensional, all of it"s bases must have the same # of vectors. This works for arbitrary bases too not just the standard bases. Let v be an n-dimensional vector space, and let {v1, v2, , vn} be any basis. a) b) If a set in v has more than n vectors, then it is linearly dependent. If a set in v has fewer than n vectors, then it does not span v.