Page 37 - 35Linear Algebra
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2








                                                 Systems of Linear Equations






                   2.1     Gaussian Elimination


                   Systems of linear equations can be written as matrix equations. Now you
                   will learn an efficient algorithm for (maximally) simplifying a system of linear
                   equations (or a matrix equation) – Gaussian elimination.



                   2.1.1    Augmented Matrix Notation

                   Efficiency demands a new notation, called an augmented matrix, which we
                   introduce via examples:
                      The linear system

                                                   x + y =      27
                                                  2x − y =      0 ,
                   is denoted by the augmented matrix



                                                    1    1 27
                                                                 .
                                                    2 −1     0
                   This notation is simpler than the matrix one,



                                               1    1    x       27
                                                             =        ,
                                               2 −1      y        0
                   although all three of the above denote the same thing.


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