SOLVING SOME PROBLEMS OF LINEAR ALGEBRA WITH COMPUTATIONS

Abstract

This thesis provides a computational solution for some problems in Linear Algebra, giving many examples and applications. I considered the computational solution that depends on maple sofiware, version 9 which is distributed in June 2003. To deal with any math soltware, you have to use packages and commands to display results. A package is a collection of routines (and perhaps other data) that are collected together in some way. Typically a package provided a range of functionality for solving problems in some well-defined problem domain. The scope of a package may be quite wide or very small. The package must be writ- ten afier the " with " command, which is an interactive package management utilities. and is effective only at the top level. The packages which were used in this text are : O plots I is a graphics package. 0 linalg 1 is a linear algebra package based on array data structures. 0 Linear Algebra : is a linear algebra package based on rtable data structures. 6 The "rrab/e( )" function is the low level routine which is used by maple to build an array. a matrix and a vector. I student[LinearAlgebra]: is a subpackage from LinearAlgebra package which has three princ- ipals components : interactive, visualization and matrix computation Each package provided many commands to activate the functions that the package is based on. A command is a direct order for a certain problem to be solved. a command can be short or a long stat- ment. The command is in red ( input ), and the result is in blue ( output). To display the result, end the command's statement with a semicolon. otherwise end the statement with a colon. l explained each co- mmand in its location when it has been used.