$\"\"$

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(a)

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Caluculate the $\"\"$ .

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Let $\"\"$ , then $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b)

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Adjoint the first two columns to right of the $\"\"$ .

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$\"\"$

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Sum of the product along the indicated downward diagonals is

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$\"\"$ .

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Sum of the product along the indicated upward diagonals is

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$\"\"$ .

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Diffeerence between the sum of downward diagonals and sum of upward diagonals is

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(c)

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Result of $\"\"$ : By using technical method $\"\"$ .

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Result of $\"\"$ : By using diagonal method $\"\"$ .

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Compare the results $\"\"$ and $\"\"$ .

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There is no change in the value of $\"\"$ in both the cases.

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$\"\"$

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(d)

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The general matrix is $\"\"$ .

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Sum of the product along the indicated downward diagonals is

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$\"\"$ .

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Sum of the product along the indicated upward diagonals is

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$\"\"$ .

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Diffeerence between the sum of downward diagonals and sum of upward diagonals is

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(e) No.

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The method of finding the determinant of the $\"\"$ matrix is lengthy process, hence it is not possible to find the determinant of the $\"\"$ matrix using diagonal method.

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Consider a $\"\"$ matrix.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ .

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(c) same answers $\"\"$ and $\"\"$ .

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(d) $\"\"$ .

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(e) No. Sample example $\"\"$ .