$\"\"$

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The matrix is $\"\"$ .

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Create the doubly augumented matrix $\"\"$ .

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$\"\"$

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Apply elementary row operations to write the matrix in reduced row- echelon form.

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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 first two columns are identity matrix, therefore $\"\"$ has an inverse and $\"\"$ .

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$\"\"$

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Check :

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Conform that $\"\"$ .

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(a)

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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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(b)

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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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$\"\"$ has an inverse and $\"\"$ .