Linear Independence

Linear independence is a property of Vector Spaces.

Vector space $S$ has elements $\{s_1,s_2,\dots ,s_p\}$ and is linearly independent if the equation

$$X_1{s}_1+x_2{s}_2+\cdots +x_p{s}_p=\vec{0}$$

has only the zero trivial solution $(x_1=x_2=\cdots =x_p=0)$.

If a system is not linearly independent, is it linearly dependent

Note: if the zero vector is in the set, the set is automatically linearly dependent