# Linear Algebra Examples

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Step 1
Move all terms containing variables to the left side of the equation.
Subtract from both sides of the equation.
Subtract from both sides of the equation.
Step 2
Move all terms containing variables to the left side of the equation.
Subtract from both sides of the equation.
Add to both sides of the equation.
Step 3
Subtract from both sides of the equation.
Step 4
Subtract from both sides of the equation.
Step 5
Write the system of equations in matrix form.
Step 6
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 ).
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 ).
Step 7
Use the result matrix to declare the final solutions to the system of equations.
Step 8
This expression is the solution set for the system of equations.
Step 9
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.