MATH1002 Lecture 9: Bases, dimension, linear transformations
24 Jul 2018
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Document Summary
We combine two notions define the basis of a of linear independence and span to subspace . S the vectors span s is linearly independent them-a. A basis is a a minimal least spanning collection of vectors in. S number of vectors required to span maximal vectors in. S linearly independent collection choose the one with the most elements. S ) of and lg the standard unit vectors span rn . Hence they form e~i a eez , basis en for r in rn called are the lin . indep . standard basis . eg show. I ] } is a basis for r " [ x any are vector in there a. 2 vectors ? afzltb 1,2]=[ y ] ? fjalxy ] retired. R2 . the given vectors span: recall that for u~ , I ] are not parallel , the vectors are linearly independent . So a subspace can have multiple bases eg find a basis for.
