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Using Elementary Row Operations to Solve Systems of Linear Equations

- The goal is to find values for variables that satisfy all equations simultaneously, even in complex systems with multiple variables and equations *1* *2* .

- Three elementary row operations can be used to manipulate matrices without changing the solutions: dividing a row by a constant, adding a multiple of one row to another, and swapping rows *3* *4* *5* .

- These operations provide a systematic method to find solutions to linear systems by transforming matrices, whether in matrix notation or not *6* *7* *8* .