# Precalculus Examples

,

Step 1

Step 2

Step 3

Write the system of equations in matrix form.

Step 4

Step 4.1

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

Step 4.1.1

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

Step 4.1.2

Simplify .

Step 4.2

Perform the row operation to make the entry at a .

Step 4.2.1

Perform the row operation to make the entry at a .

Step 4.2.2

Simplify .

Step 4.3

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

Step 4.3.1

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

Step 4.3.2

Simplify .

Step 4.4

Perform the row operation to make the entry at a .

Step 4.4.1

Perform the row operation to make the entry at a .

Step 4.4.2

Simplify .

Step 5

Use the result matrix to declare the final solutions to the system of equations.

Step 6

The solution is the set of ordered pairs that makes the system true.

Step 7

The vector is in the column space because there is a transformation of the vector that exists. This was determined by solving the system and showing there is a valid result.

In the Column Space