The equation are $\"\"$ .

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Above equation can write matrix form.

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$\"\"$

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$\"\"$

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use doolittle method $\"\"$

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Where $\"\"$

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$\"\"$

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$\"\"$

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Comparing on each side

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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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$\"\"$

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$\"\"$

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$\"\"$

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Let $\"\"$

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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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Therefore, $\"\"$

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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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