Lecture-09 - Linear Algebraic Equations Part 3 An equation...

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2/16/10 1 Linear Algebraic Equations Part 3 An equation of the form ax+by+c=0 or equivalently ax+by=- c is called a linear equation in x and y variables. ax+by+cz=d is a linear equation in three variables, x, y , and z . Thus, a linear equation in n variables is a 1 x 1 +a 2 x 2 + … +a n x n = b A solution of such an equation consists of real numbers c 1 , c 2 , c 3 , … , c n . If you need to work more than one linear equations, a system of linear equations must be solved simultaneously. Noncomputer Methods for Solving Systems of Equations • For small number of equations (n 3) linear equations can be solved readily by simple techniques such as “method of elimination.” • Linear algebra provides the tools to solve such systems of linear equations. • Nowadays, easy access to computers makes the solution of large sets of linear algebraic equations possible and practical. Gauss Elimination Solving Small Numbers of Equations • There are many ways to solve a system of linear equations: – Graphical method – Cramer’s rule – Method of elimination – Computer methods For n 3 Graphical Method For two equations: Solve both equations for x 2: Plot x 2 vs. x 1 , the intersection of the lines present the solution. 2
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This note was uploaded on 03/20/2010 for the course CHEN 313 taught by Professor Seminario during the Spring '07 term at Texas A&M.

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Lecture-09 - Linear Algebraic Equations Part 3 An equation...

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