Gauss Elimination in Formula Form

The Gauss elimination is accomplished by a series of elementary operations that do not alter the solution of the equation. Thc.se operations are  

Any equation in the set can be multiplied (or divided) by a nonzero scalar without affecting the solution. 

Any two equations can interchange po.sitions within the set without affecting the 

Two matrices that can be obtained from each other by successive application of the above elementary operations are said to be equivalent matrices. The rank and determinant of these matrices are unaltered by the application of elementary operations. 

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