Linear Indepence and Dependence

Last updated Feb 23, 2022 Edit Source

• Math linear

A set of vectors are linearly dependent if:

$$\begin{bmatrix} v_1 & v_2 & v_3 & … & v_n \end{bmatrix} x = 0$$

only has the Trivial Solution as a solution.

It can also be said that the set is linearly dependent if a vector in the set is a linear combination of one or more vectors in the set.

Linear dependency is also present if given a set of vectors ${v_1, v_2, …, v_n}$, the equation $c_1v_1 + c_2v_2 + … + c_nv_n = 0$ can be satisfied where not all the constants are 0.

If there are more than $n$ vectors in the set, each of which of size $\mathbb{R}^n$ cannot be linearly independent.

If the zero vector is in the set, it is linearly dependent