What happens when vectors are added to a set of linearly dependent vectors?

When vectors are added to a set of linearly dependent vectors, the resulting set remains linearly dependent. This is because linear dependence means that one or more vectors in the set can be expressed as a linear combination of the others. If new vectors are introduced to this collection of vectors, they may not provide any new direction in the vector space, thereby preserving the linear dependence of the overall set.

To put it another way, since the original set already has a dependency among its vectors, adding more vectors cannot change this characteristic. In some cases, the newly added vectors may even be expressible as a linear combination of the previously existing vectors, further reinforcing the dependence within the set.

The idea that the set could become linearly independent when new vectors are added contradicts the fundamental concept of linear dependence. Therefore, it stands true that the addition of vectors to a linearly dependent set keeps the whole set dependent.