Lecture Notes 2

# Lecture Notes 2 - Lecture02 Lecture 02 Systems of Linear...

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Lecture02 1 September 06, 2007 Outline: 1) The relationship between systems of linear equations and Linear Combinations of vectors 2) The relationship between systems of equations and Ax =b 3) Basic rules of Matrix-vector products Ax as linear combinations of vectors 4) Ax =b : the fundamental issues 5) Solving linear systems: Introduction to Gaussian Elimination Lecture 02: Systems of Linear Equations and Ax =b Systems of linear Equations A simple example: x - y = 1 2x + y = 5 Solution by "elimination" and "back-substitution": The geometry of Linear Systems: the "row" picture x - y = 1 2x + y = 5 x - y = 1 2x + y = 5 The geometry of Linear Systems: the "column" picture Linear systems of equations as Linear Combinations of vectors Is equivalent to: Interpretation: solving linear systems is equivalent to finding linear combination of vectors that add up to another vector The geometry of Linear Systems: the "column" picture x - y = 1 2x + y = 5 3x3 problems (3 equations, 3 unknowns):

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## This note was uploaded on 06/02/2010 for the course APMA APMA E3101 taught by Professor Spiegelman during the Fall '07 term at Columbia.

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Lecture Notes 2 - Lecture02 Lecture 02 Systems of Linear...

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