# Linear Algebra Examples

,

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

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

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 4

Since the resulting system is consistent, the vector is an element of the set.