Chapter-09

# Chapter-09 - Linear Algebraic Equations Part 3 An equation...

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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.

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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.
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Gauss Elimination Chapter 9 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: 2 2 22 1 21 1 2 12 1 11

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

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