The linear span of a set of vectors is all of it's constituting linear combinations. The span of vectors is typically denoted as . Given a set of vectors, their span is defined as follows

Determining if a Vector is in the Span of Others

Given a vector we can determine if it is in the span of , by checking if the following equation has any non trivial solutions

Example

Given the following set of vectors

determine if the span of them contains .

First we setup the equation

Then the equation is converted into the standard linear system form

we can then perform gaussian elimination to get our final solutions