$\"\"$

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Guass-jordan elimination method :

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The system of equations are

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$\"\"$

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Write the equations into matrix form $\"\"$ .

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Where $\"\"$ is coefficient matrix, $\"\"$ is variable matrix and $\"\"$ is constant matrix.

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Solve the equations in Gauss-Jordan method.

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$\"\"$

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The augmented matrix is $\"\"$ .

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$\"\"$ .

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$\"\"$

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The augment matrix is $\"\"$ .

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Apply elementary row operations to obtain a reduce the row-echelon form.

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Here $\"\"$ are represents first row, second row and third row .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Write the corresponding system of the linear equations for the reduced row-echelon form of the augmented matrix is

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$\"\"$ .

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Because the value of $\"\"$ not determined, this system has infinitely many solutions.

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Solve for $\"\"$ , $\"\"$ in terms of $\"\"$ .

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$\"\"$ .

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$\"\"$ where $\"\"$ is any real number.

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$\"\"$

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$\"\"$ where $\"\"$ is any real number.