Determine whether the set of vectors will span r3?

Since each vector is a member of , the vectors will span if they form a basis for , which requires that they be linearly independent of one another.

To show this, you have to establish that the only linear combination of the three vectors  that gives the zero vector occurs for scalars .



Solving this, you'll find that , so the vectors are indeed linearly independent, thus forming a basis for and therefore they must span .