# 2 - MATHEMATICS 54 Professor Constantin Teleman 9/1/09...

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Unformatted text preview: MATHEMATICS 54 Professor Constantin Teleman 9/1/09 Lecture 2 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 Is everyone fine with your section enrollment? I forgot to mention last time that there is a webpage for this course, which can be accessed through a link on my old web page: math.berkeley.edu/~teleman . You can find the syllabus and check updated homework assignments. Regarding to the homework, I highly recommend you do them well because they are very similar to the questions on the exams. LECTURE Last time we have talked about three sections: 1. Define the echelon form and reduced echelon form of a matrix. 2. Wrote down the general solution of a linear system from the reduced echelon form. 3. Gaussian elimination algorithm to echelon form. We havent finished talking about the third section. Today we will finish the last section and move on to new sections. We will discuss solutions of linear system (qualitative properties), start developing matrix and vector algebra (=symbolic language +concepts that are useful for linear equation). (Left over) From a matrix in echelon from to the reduced echelon for: 1. Rescale every non-zero row to make the point =1. 2. Starting from the bottom row, add multiples of each row to the row above it so as to cancel the entries above the pivots. Example: f e r r f e . . . 3 2 1 2 1 1 .) . ( 48 32 16 7 5 3 1 15 13 11 9 7 5 3 1 Comments on row reduction: Sometimes you want to remember the original pivots....
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## This note was uploaded on 12/01/2009 for the course MATH 54 taught by Professor Chorin during the Spring '08 term at University of California, Berkeley.

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2 - MATHEMATICS 54 Professor Constantin Teleman 9/1/09...

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