(a) If vectors u, v and w are linearly independent, will (u+v), (v+w) and (u+w) also be linearly independent? Justify your answer.

(b)If vectors u, v and w are linearly independent, will (u-v), (v-w) and (u-w) also be linearly independent? Justify your answer.

The answer in the back of the book is (a) yes. (b) no

Any help on why this is?

Cheers