MAT 1341 Lecture 11: More on basis and dimension
15 Nov 2016
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Recall: size of any li set in v size of any spanning set in v. Let v be a vector space and be a set of vectors in v. is called a basis of v if it is linearly independent and it spans v. Definition a basis is: a linearly independent spanning set of v the biggest possible li set in v the smallest possible spanning set in v a) b) c) 9. 5 examples finite basis, it is infinite dimensional. If v has a finite basis then the dimension of v is n, dim(v)=n. If v doesn"t have a dim( )=2 because {(1,0),(0,1)} is a basis of dim( )=3, dim( )=n dim( dim( dim( dim: f. Right away, we know that is a spanning set for w, and that"s it"s linearly. Find a basis for so dim(l)=3. independent (which we verified earlier). Therefore it"s a basis for w and dim(w)=3.
