# Linear Dependence and Linear Independence Vectors

__Linear Dependence__**:**

Let be a vector space and let be a finite subset of . Then is said to be linearly dependence if there exist scalar, not all zero, such that

__Linear Independence__**:**

Let be a vector space and let be a finite subset of . Then is said to be linearly independence if,

Holds only when .

An infinite subset of is said to be linearly independence if every finite subset is linearly independent, otherwise it is linearly dependence.

__Example 1__**:** Show that the system of three vectors , , of is linearly dependent.

__Solution__**:** For .

Therefore, the given system of vectors in linearly dependence.

__Example 2__**:** Consider the vector space and the subset of . Prove that is linearly independent.

__Solution__**:** For .

This shows that if any linear combination of elements of is zero then the coefficient must be zero. is linearly independent.