Check if Linearly Dependant

This examples goes over determining whether a subspace of vectors are linearly dependant.

Problem

Given:
Determine whether are Linearly Dependant.

Solution

This is asking us to determine if there exists other than such that . To figure this out we construct the following compact linear system:
Performing Gaussian elimination on the augmented matrix we get:
This tells us that are in fact linearly dependant since there are infinite solutions other than the solution.