# Berkeley MATH 110 - Lecture Notes (6 pages)

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## Lecture Notes

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Lecture Notes

- Pages:
- 6
- School:
- University of California, Berkeley
- Course:
- Math 110 - Linear Algebra

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Math 110 Fall 05 Lectures notes 1 Aug 29 Monday Name class URL www cs berkeley edu demmel ma110 on board See Barbara Peavy in 967 Evans Hall for all enrollment issues All course material will be on the web page If this is inadequate please send me email and I will put copies at Copy Central Northside Read Course Outline on web page for course rules and grading policies You are responsible for reading this and knowing the rules Text which we will follow fairly closely Linear Algebra 4th Edition by Friedberg Insel Spence same as last semester Topics following table of contents Chap 1 Vector spaces vectors and their basic properties Chap 2 Linear transformations matrices and their basic properties Chap 3 Elementary Matrix Operations quickly Chap 4 Determinants Chap 5 Diagonalization eigenvalues and vectors Chap 6 Inner products orthgonality singular value decomposition Chap 7 Jordan Form generalizations of eigenvectors Examples why is linear algebra important Linear Equations Consider new Bay Bridge how is it designed How do they know it will be strong enough to hold up the traffic If you imagine a car sitting on the end of a beam you can write a simple relationship F force from weight of car on bridge k stiffness of beam x how much beam bends So if you know the weight of the car and the stiffness of the beam you can solve one linear equation in one unknown F kx for x F k to get the amount the bridge bends and compare that to how much you are willing to let it bend In a real bridge there are many cars many beams and many x s describing how each beam bends and the the beams are connected So instead of of 1 linear equation in 1 unknown you get thousands of linear equations in thousands of unknowns which civil engineers have to solve The same process applies to any important structures buildings airplanes cars certain computer chips See CE 130 ME 104 1 All radio light and other electromagnetic radiation in free space satisfy a system of linear equations called Maxwell s

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