How to check linear independence

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How can I check the linear independence of my variables?

I have this system $Ax=b$ where $A$ is a $N \times 4$ matrix.

I want to check the linear independence between the 4 variables in matrix $A$.

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It is not clear what you mean by "linear independence between the 4 variables". If you want the solution to be unique, the rank of both $A$ and $[A|b]$ needs to be $4$.