# Linear Algebra Examples

Determine if the Vector is in the Span of the Set
,
Step 1
Assign the set the name and the vector the name .
Step 2
Set up a linear relation to see if there is a non-trivial solution to the system.
Step 3
Find the reduced row echelon form.
Step 3.1
Write the vectors as a matrix.
Step 3.2
Write as an augmented matrix for .
Step 3.3
Perform the row operation to make the entry at a .
Step 3.3.1
Perform the row operation to make the entry at a .
Step 3.3.2
Simplify .
Step 3.4
Perform the row operation to make the entry at a .
Step 3.4.1
Perform the row operation to make the entry at a .
Step 3.4.2
Simplify .
Step 3.5
Perform the row operation to make the entry at a .
Step 3.5.1
Perform the row operation to make the entry at a .
Step 3.5.2
Simplify .
Step 3.6
Perform the row operation to make the entry at a .
Step 3.6.1
Perform the row operation to make the entry at a .
Step 3.6.2
Simplify .
Step 3.7
Perform the row operation to make the entry at a .
Step 3.7.1
Perform the row operation to make the entry at a .
Step 3.7.2
Simplify .
Step 3.8
Perform the row operation to make the entry at a .
Step 3.8.1
Perform the row operation to make the entry at a .
Step 3.8.2
Simplify .
Step 4
Since the resulting system is consistent, the vector is an element of the set.