# Linear Algebra Examples

Step 1

Write as an augmented matrix for .

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

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 solution to the system of equations.

Step 4

Write a solution vector by solving in terms of the free variables in each row.

Step 5

Write as a solution set.