# Rewrite as a Vector Equality minus x plus two y minus three z equals one , two x plus z equals zero , three x minus four y plus four z equals two

, ,

Write the system of equations in matrix form.

Perform the row operation on (row ) in order to convert some elements in the row to .

Replace (row ) with the row operation in order to convert some elements in the row to the desired value .

Replace (row ) with the actual values of the elements for the row operation .

Simplify (row ).

Perform the row operation on (row ) in order to convert some elements in the row to .

Replace (row ) with the row operation in order to convert some elements in the row to the desired value .

Replace (row ) with the actual values of the elements for the row operation .

Simplify (row ).

Perform the row operation on (row ) in order to convert some elements in the row to .

Replace (row ) with the row operation in order to convert some elements in the row to the desired value .

Replace (row ) with the actual values of the elements for the row operation .

Simplify (row ).

Perform the row operation on (row ) in order to convert some elements in the row to .

Replace (row ) with the actual values of the elements for the row operation .

Simplify (row ).

Perform the row operation on (row ) in order to convert some elements in the row to .

Replace (row ) with the actual values of the elements for the row operation .

Simplify (row ).

Perform the row operation on (row ) in order to convert some elements in the row to .

Replace (row ) with the actual values of the elements for the row operation .

Simplify (row ).

Perform the row operation on (row ) in order to convert some elements in the row to .

Replace (row ) with the actual values of the elements for the row operation .

Simplify (row ).

Perform the row operation on (row ) in order to convert some elements in the row to .

Replace (row ) with the actual values of the elements for the row operation .

Simplify (row ).

Perform the row operation on (row ) in order to convert some elements in the row to .

Replace (row ) with the actual values of the elements for the row operation .

Simplify (row ).

Use the result matrix to declare the final solutions to the system of equations.

The solution is the set of ordered pairs that makes the system true.

Decompose a solution vector by re-arranging each equation represented in the row-reduced form of the augmented matrix by solving for the dependent variable in each row yields the vector equality.

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