Just to add to the existing responses, matrices represent linear transforms, which have many convenient properties. However, translation, that is moving things,

Just to add to the existing responses, matrices represent linear transforms, which have many convenient properties. However, translation, that is moving things, is not a linear transform. (All linear transforms must map the zero vector to itself, but if you move an object at the origin somewhere else, it's no longer at the origin.) Translation is an affine transform. Now here's the trick. You can embed your three-dimensional space into a four-dimensional space at a fixed fourth coordinate (but not zero). In this new space, translation in the original three-dimensional space is a linear transform.