# 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

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.