# Linear Algebra Examples

,
Step 1
Write as an augmented matrix for .
Step 2
Write as a linear system of equations.
Step 3
Solve the system of equations.
Step 3.1
Move variables to the left and constant terms to the right.
Step 3.1.1
Move all terms containing variables to the left side of the equation.
Step 3.1.1.1
Subtract from both sides of the equation.
Step 3.1.1.2
Subtract from both sides of the equation.
Step 3.1.2
Subtract from both sides of the equation.
Step 3.1.3
Move all terms containing variables to the left side of the equation.
Step 3.1.3.1
Subtract from both sides of the equation.
Step 3.1.3.2
Add to both sides of the equation.
Step 3.1.4
Subtract from both sides of the equation.
Step 3.2
Write the system as a matrix.
Step 3.3
Find the reduced row echelon form.
Step 3.3.1
Multiply each element of by to make the entry at a .
Step 3.3.1.1
Multiply each element of by to make the entry at a .
Step 3.3.1.2
Simplify .
Step 3.3.2
Perform the row operation to make the entry at a .
Step 3.3.2.1
Perform the row operation to make the entry at a .
Step 3.3.2.2
Simplify .
Step 3.3.3
Multiply each element of by to make the entry at a .
Step 3.3.3.1
Multiply each element of by to make the entry at a .
Step 3.3.3.2
Simplify .
Step 3.3.4
Perform the row operation to make the entry at a .
Step 3.3.4.1
Perform the row operation to make the entry at a .
Step 3.3.4.2
Simplify .
Step 3.4
Use the result matrix to declare the final solution to the system of equations.
Step 3.5
Write a solution vector by solving in terms of the free variables in each row.
Step 3.6
Write as a solution set.