$\"\"$

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(a)

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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 standard form $\"\"$ .

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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 augmented 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 and second 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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$\"\"$

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$\"\"$ and $\"\"$ .

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$\"\"$

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(b)

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The system of equations are

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$\"\"$

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Write the equations into matrix form $\"\"$ , where $\"\"$ is coefficient matrix, $\"\"$ is variable matrix and $\"\"$ is constant matrix.

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$\"\"$

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Inverse of a $\"\"$ matrix : $\"\"$ .

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Here $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Multiply $\"\"$ by $\"\"$ to solve the system.

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The solutions of system of equation $\"\"$ and $\"\"$ .

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$\"\"$

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(c)

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Cramer $\"\"$ s rule:

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The system of equations are

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$\"\"$

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Where $\"\"$ is coefficient matrix.

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$\"\"$

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Caluculate the determinant of matrix $\"\"$ .

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$\"\"$

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Because of the determinant of $\"\"$ is does not zero so,apply cramers rule.

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$\"\"$ and $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The values of $\"\"$ and $\"\"$ . $\"\"$

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(a) $\"\"$ .

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(b) The solutions of system of equation $\"\"$ and $\"\"$ .

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(c) $\"\"$ .