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Unformatted text preview: MATHEMATICS 54 Professor Constantin Teleman 9/3/09 Lecture 3 ASUC Lecture Notes Online is the only authorized notetaking service at UC Berkeley. Do not share, copy or illegally distribute (electronically or otherwise) these notes. Our studentrun program depends on your individual subscription for its continued existence. These notes are copyrighted by the University of California and are for your personal use only. D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. ANNOUNCEMENTS Student Learning Center 1. Math 54 Study Group: TTh 23pm, Room TBA (see website), will start from next week. 2. Math/ Stat Drop In: MTh 10am4pm. This week’s homework is due by next Wednesday since next Monday is a holiday. LECTURE Last time, we talked about three sections: 1. Linear combination of vectors. 2. Span or a collection of vectors. 3. Linear subspace. 4. Affine subspace 5. Relation with linear equation. These are the basic vocabulary and symbolic of calculus for solution of linear equations. A linear combination of v v v v r r r r r ... , , 3 2 1 is any vector v k v k r r v r r r ... 1 1 = , R k k k k r ∈ ... 3 2 1 . k i : The “weights” of the linear combination. The span of a collection of vectors is the set of all their linear combinations as R k k k k r ∈ ... 3 2 1 . It is a set of vectors and it is a subset of R n . r v + r w is a particular linear combination. Here is another linear combination: The typical affine subspace in R 2 is obtained by translations of the line { k r w ⏐ k ∈ R} by 2 r v ....
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 Spring '08
 Chorin
 Math, Linear Algebra, Vector Space, ax, Linear combination, rr rr, Linear subspace

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