It's not clear from your question whether you want to prove that
any singular matrix has linearly dependent rows (or colummns), or rather prove a
particular matrix has linearly dependent rows.
If the latter, you may use the fact that the following statements are equivalent for a square matrix:
(i) The matrix is singular.
(ii) The matrix has linearly dependent rows (and columns).
(iii) The determinant of the matrix is zero.
Thus, it will suffice to compute the determinant of the matrix, and if it's zero, that immediately implies (ii).
matrix determinant