$\"\"$

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The standard parabola equation is $\"\"$ .

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The parabola passes through the three points are $\"\"$ and $\"\"$ .

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(a) Write the system of equations. \ \

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Substitute for $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute for $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute for $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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The system of equations $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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(b) The system of equations are

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$\"\"$

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$\"\"$

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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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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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$\"\"$

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$\"\"$ .

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

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By using matrices solution of the system is $\"\"$ .

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$\"\"$

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(c)

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

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$ .

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The parabola equation is $\"\"$ .

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$\"\"$

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(a)

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The system of equations $\"\"$ , $\"\"$ and $\"\"$ .

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(b)

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The matrices values are $\"\"$ , $\"\"$ and $\"\"$ .

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(c)

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The parabola equation is $\"\"$

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