state and prove linear equation
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Answer:
Theorem. A system of linear equations either has no solutions or has exactly one solution or has infinitely many solutions. A system of linear equations has infinitely many solutions if and only if its reduced row echelon form has free unknowns and the last column of the reduced row echelon form has no leading 1's. It has exactly one solution if and only if the reduced row echelon form has no free unknowns and the last column of the reduced row echelon form has no leading 1. It has no solutions if and only if the last column of the reduced row echelon form has a leading 1.\
Proof. Indeed, consider the reduced row-echelon form of our system of equations.
Suppose first that it contains an equation with zero left side and non-zero right side. It must have the form
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Step-by-step explanation:
prove linear equation it is a linear equation..