Question

If {u, v, w} is a basis of V3 (R), show that { u+v , v+w , w+u } is also a basis of V3(R).​

Answer 1

Answer:

Answer:are three vectors in R3, then (~u ~v) w~= u 1 u 2 u 3 v 1 v 2 v 3 w 1 w 2 w 3 : Proof. We have already seen that ~u u~v= ^ ^{ ^| k u 1 2 u 3 v 1 v 2 v 3 : If one expands this determinant and dots with w~, this is the same as replacing the top row by (w 1;w 2;w 3), (~u ~v) w~= w 1 w 2 w 3 u 1 u 2 u 3 v 1 v 2 v 3 : Finally, if we switch the rst row.