# Linear Algebra Examples

, ,
Step 1
Assign the set to the name to use throughout the problem.
Step 2
Create a matrix whose rows are the vectors in the spanning set.
Step 3
Find the reduced row echelon form of the matrix.
Step 3.1
Swap with to put a nonzero entry at .
Step 3.2
Multiply each element of by to make the entry at a .
Step 3.2.1
Multiply each element of by to make the entry at a .
Step 3.2.2
Simplify .
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
Multiply each element of by to make the entry at a .
Step 3.4.1
Multiply each element of by 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 4
Convert the nonzero rows to column vectors to form the basis.