# What does it mean for a linear system to be linearly independent?

##### 1 Answer

Oct 22, 2015

Consider a set S of finite dimensional vectors

Let

Now consider the vector equation

If the only solution to this equation is **linearly independent.**

If however other solutions to this equation exist in addition to the trivial solution where all the scalars are zero, then the set S of vectors is said to be linearly dependant.