# Linear Algebra Examples

, ,

Step 1

Write the system of equations in matrix form.

Step 2

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

Perform the row operation to make the entry at a .

Step 2.3.1

Perform the row operation to make the entry at a .

Step 2.3.2

Simplify .

Step 2.4

Multiply each element of by to make the entry at a .

Step 2.4.1

Multiply each element of by to make the entry at a .

Step 2.4.2

Simplify .

Step 2.5

Perform the row operation to make the entry at a .

Step 2.5.1

Perform the row operation to make the entry at a .

Step 2.5.2

Simplify .

Step 2.6

Multiply each element of by to make the entry at a .

Step 2.6.1

Multiply each element of by to make the entry at a .

Step 2.6.2

Simplify .

Step 2.7

Perform the row operation to make the entry at a .

Step 2.7.1

Perform the row operation to make the entry at a .

Step 2.7.2

Simplify .

Step 2.8

Perform the row operation to make the entry at a .

Step 2.8.1

Perform the row operation to make the entry at a .

Step 2.8.2

Simplify .

Step 2.9

Perform the row operation to make the entry at a .

Step 2.9.1

Perform the row operation to make the entry at a .

Step 2.9.2

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.