# Linear Algebra Examples

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Move all terms not containing a variable to the right side of the equation.
Move to the right side of the equation because it does not contain a variable.
Move all terms not containing a variable to the right side of the equation.
Move to the right side of the equation because it does not contain a variable.
Subtract from to get .
Move all terms not containing a variable to the right side of the equation.
Move to the right side of the equation because it does not contain a variable.
Write the system of equations in matrix form.
Find the reduced row echelon form of the matrix.
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 ).
Use the result matrix to declare the final solutions to the system of equations.
This expression is the solution set for the system of equations.
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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