Linear Independence of Sets in a Linear Space

[mrs.malfoy]

Let V be a linear space and u, v, w \in V. Show that if {u, v, w} is linearly independent then so is the set {u, u+v, u+v+w}

 

[HallsofIvy]

Let V be a linear space and u, v, w \in V. Show that U \cap V is not equal to {O_V}

?? What is U?

 

[CompuChip]

Can you explain your notation?
So u is an element of the linear space V, but what is U?
What is O_V, is it the zero element in V?