My understanding of linear independance is that if you have a unique solution after rref, it's linear independant. If you have multiple solutions or no solution, it's not linear ...
SIAM Journal on Numerical Analysis, Vol. 44, No. 6 (2006), pp. 2389-2407 (19 pages) Characterizing the linear and local linear independence of the functions that span a linear space is a key task if ...
Description: First-order equations, higher-order linear equations, initial and boundary value problems, power series solutions, systems of first-order equations, Laplace transforms, applications.
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