2 4 two systems are same set of solutions said to be equivalent if they have the a system can be solved by writing each equivalent other a to series of systems one after the the previous system the following operations called elementary row operations representing a a matrix can roughly be performed on system of linear equations interchange 2 multiply one nonzero add a multiple of one row to rows row by a constant another row operations are performed on represent equations rows not columns as rows 2 4 the goal of performing gauss Jordan row operations is to have a matrix in reduced row echelon form a matrix is said to be in reduced row echelon form if it satisfies each of all zero rows the following conditions are below all nonzero rows if they exist the first from the left nonzero entry leading l the 1 the right of for all in each that row leading is row must be a each leading I in the rows above called is to it each leading i is the only nonzero entry in its column 2 4 row operations one way to solve a system of GJ the resulting system of equations has the same solution as the original system to produce a matrix linear equations is to perform in RREF 1 write the corresponding augmented matrix for the given system of linear equations 2 interchange vows in the number nonzero if necessary to first row first a obtain column 3 use a row operation column first row first to make a l the entry in the 4 use a row operation to make the column O first all other entries in
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