3 - MATHEMATICS 54 Professor Constantin Teleman 9/3/09...

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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 note-taking service at UC Berkeley. Do not share, copy or illegally distribute (electronically or otherwise) these notes. Our student-run 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 2-3pm, Room TBA (see website), will start from next week. 2. Math/ Stat Drop In: M-Th 10am-4pm. This weeks 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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3 - MATHEMATICS 54 Professor Constantin Teleman 9/3/09...

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