What are Linear Dependence and Independence

A set of vectors is linearly dependent if some linear combination of the vectors is equal to zero where at least one coefficient (of the vectors) is non-zero.

$$\begin{array}{r}B=\{{\vec{v}}_1,..,{\vec{v}}_k\}\subseteq R^n\\ c_1{\vec{v}}_1+...+c_n{\vec{v}}_n=0\end{array}$$

Where at least one $c_i\ne 0$.

• If all of the coefficients are 0, then the set is linearly independent.
• This is the trivial solution of the homogenous equation where all the coefficients are 0.