Matrix associated to a system

 Each system

    has two associated matrices:

    

Example:

       

Then the elementary operations are:
–To exchange two rows:  Ri ↔ Rj
–To substitute a row by a linear combination of all the rows:

            Ri↔ k1R1+k2R2+…+kiRi+…kmRm, ki ≠ 0, kj are real numbers, j = 1, 2, ….m

 

Exercise. Find the associated matrices to these systems:

 

 

 

 

Solutions:

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