# Precalculus Examples

Determine if the Vector is in the Column Space
,
Step 1
Step 2
Step 3
Write the system of equations in matrix form.
Step 4
Find the reduced row echelon form.
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