Proving Linear Dependency

Show that if {v1, v2, v3} is a linearly dependent set of vectors in a vector space V, and v4 is any vector, then {v1, v2, v3, v4} is also linearly dependent.

If I set up a matrix I would end up with a row of 0's in echelon form meaning there is no unique solution, so if I add a 4th column to that matrix would I obtain a row of 0's again, still proving that there is no unique solution, which means it is linearly dependent? If so could somebody set it up for me to see, and if not, could somebody explain how I would go about doing this.

Thanks