Step 1:

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The system of linear equations are $\"\"$

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

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

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$\"\"$

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Solve the equations in Gaussian elimination method.

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The augmented matrix is $\"\"$ .

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$\"\"$

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$\"\"$ are represents first row and second row.

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$\"\"$

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$\"\"$

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Eliminate first row and second coloumn.

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$\"\"$

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$\"\"$

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$\"\"$

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Solution:

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The system of equations values are $\"\"$

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(2)

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The addition matrix is $\"\"$

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Simplify the matrix operation.

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$\"\"$

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$\"\"$

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(3) The matrix $\"\"$

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Find $\"\"$ .

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The first matrix is $\"\"$ and second matrix is $\"\"$ ,So its multipication possible.

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$\"\"$

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$\"\"$

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(4)

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The equation is $\"\"$

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Identify the conic section equation.

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$\"\"$

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The conic section equation is $\"\"$

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(5)

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Step 1:

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The infinite sequence of recursion formula is

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$\"\"$

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Find the first four terms.

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Substitute $\"\"$ in the recursion formula.

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$\"\"$

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Substitute $\"\"$ in the recursion formula.

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$\"\"$

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Substitute $\"\"$ in the recursion formula.

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$\"\"$

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Substitute $\"\"$ in the recursion formula.

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$\"\"$

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Find eight term.

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Substitute $\"\"$ in the recursion formula.

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$\"\"$

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Solution:

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The infinite sequences of first four and eighth terms,

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$\"\"$