If you fill an $n\times n$ matrix with random entries, than you’ll almost surely end up with a full-rank matrix. Also, any matrix that is constructed with real and continuous data (e.g., sensor input) will also be almost surely of full rank even if the underlying should have lead to linearly dependent columns/rows. Further, if we do not use exact arithmetic but, say, floating point arithmetic, our $\mathbf A$ will almost surely be somewhat perturbed, especially if it is a result…