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
Multiply each element of by to make the entry at a .
Step 3.1.1
Multiply each element of by to make the entry at a .
Step 3.1.2
Simplify .
Step 3.2
Perform the row operation to make the entry at a .
Step 3.2.1
Perform the row operation 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
Multiply each element of by to make the entry at a .
Step 3.6.1
Multiply each element of by 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 3.9
Perform the row operation to make the entry at a .
Step 3.9.1
Perform the row operation to make the entry at a .
Step 3.9.2
Simplify .
Step 4
Convert the nonzero rows to column vectors to form the basis.