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Systems of linear equations can be solved by using elementary row operations to manipulate the augmented matrix into a row reduced echelon form or a simplified form where the equations can easily be solved using back substitution.
In this second example, the system of equations does not have a solution. During the row operations we encounter a mathematical contradiction which tells us the system has no solution.
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Linear Algebra Example Problems - Solving Systems of Equations (2/3) | NatokHD