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Gauss-Jordan Elimination for systems of linear equations Ú Û Ü $B C #D Å“ ” D $C D Å“ $ #B C D Å“

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Gauss-Jordan Elimination for systems of linear equations
Ú
Û
Ü
$B C #D Å“ ”
D $C D Å“ $

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B C D Å“ ”

Write in matrix form:
Then using elementary row operations we should obtain a reult that looks like the following:
Ô × Ô ×
Õ Ø Õ Ø
$ ” # l ” ” ! ! l+
” $ ” l $ ! ” ! l,

” ” l ” ! ! ” l-

Ä Ð<>
You only want to use one row operation at a time.
Elementary Row Operations

  1. Interchange any two rows.
    V Ç V à 3 4
    this implies that the i row is interchanged with the j row. >2 >2
    This operation is done specifically to obtain the number ” ” in a given location. ”
  2. Multiply a row by a nonzero constant. Use the result to replace the same row.
    -V Ä V 3 3 ;
    this implies that the i row has been multiplied by a constant and the i row is replaced with the result. >2 >2
    This operation is also done to obtain the number ” ” ” in a given location.
    Please note that is the reciprocal of the entry th – at was originally in the location that is to be replaced by ” .” ”
  3. Multiply a row by a nonzero constant. Add the result to another row. This combination will replace the latter row.
    5V V Ä V à 3 4 4
    This implies that the i row has been multiplied by a nonzero constant and the result has been added to the j row. >2 >2
    This sum will be used to replace the entries in the j row. >2
    This operation is done specifally to obtain the number ” ” in a given location. !
    Please note that is the opposite of the entry that 5 was originally in the location that is to be replaced by ” .” !
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