# Precalculus Examples

Determine if the Vector is in the Column Space
,
Write the system of equations in matrix form.
Row reduce.
Perform the row operation on (row ) in order to convert some elements in the row to .
Replace (row ) with the row operation in order to convert some elements in the row to the desired value .
Replace (row ) with the actual values of the elements for the row operation .
Simplify (row ).
Perform the row operation on (row ) in order to convert some elements in the row to .
Replace (row ) with the row operation in order to convert some elements in the row to the desired value .
Replace (row ) with the actual values of the elements for the row operation .
Simplify (row ).
Perform the row operation on (row ) in order to convert some elements in the row to .
Replace (row ) with the row operation in order to convert some elements in the row to the desired value .
Replace (row ) with the actual values of the elements for the row operation .
Simplify (row ).
Use the result matrix to declare the final solutions to the system of equations.
Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
The solution is the set of ordered pairs that makes the system true.
There is not a transformation of the vector that exists because there was no unique solution to the system of equations. Since there is no linear transformation, the vector is not in the column space.
Not in the Column Space

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