When you have a standard vector space like Q3 with some vectors, we can check whether they are linearly independent or not.
v1 = vector(QQ, [0,1,-3])
v2 = vector(QQ, [4,1,0])
V = QQ^3
relations = V.linear_dependence([v1, v2]); relations
Now my question is the following is there a direct method to check whether a couple of matrices are linearly independent in the set of n×n matrices over R?