How to check if m n-sized vectors are linearly independent?

Question

Disclaimer
This is not strictly a programming question, but most programmers soon or later have to deal with math (especially algebra), so I think tha

Answer 1

If m, you will have to do some operation on them (there are multiple possibilities: Gaussian elimination, orthogonalization, etc., almost any transformation which can be used for solving equations will do) and check the result (eg. Gaussian elimination => zero row or column, orthogonalization => zero vector, SVD => zero singular number)

However, note that this question is a bad question for a programmer to ask, and this problem is a bad problem for a program to solve. That's because every linearly dependent set of n vectors has a different set of linearly independent vectors nearby (eg. the problem is numerically unstable)