What is the fastest way to check whether a system of linear equations has a solution?
I know that LinearSolve can solve this problem, but if you don't need to know the what the solution is, but only need to judge the existence, is there a more efficient method? The way to calculate rank seems to be slower.
Specifically, the equation can be given by the coefficient matrix $A \in \mathbb{R}^{m\times n} $ and the column vector b, where m and n are large (at least thousands). They are both in the form of SparseArray.
