# Linear Algebra Examples

,
Step 1
Write the system of equations in matrix form.
Step 2
Find the reduced row echelon form.
Step 2.1
Multiply each element of by to make the entry at a .
Step 2.1.1
Multiply each element of by to make the entry at a .
Step 2.1.2
Simplify .
Step 2.2
Perform the row operation to make the entry at a .
Step 2.2.1
Perform the row operation to make the entry at a .
Step 2.2.2
Simplify .
Step 2.3
Multiply each element of by to make the entry at a .
Step 2.3.1
Multiply each element of by to make the entry at a .
Step 2.3.2
Simplify .
Step 2.4
Perform the row operation to make the entry at a .
Step 2.4.1
Perform the row operation to make the entry at a .
Step 2.4.2
Simplify .
Step 3
Use the result matrix to declare the final solutions to the system of equations.
Step 4
The solution is the set of ordered pairs that makes the system true.
Step 5
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.