- #1
Aristotle
- 169
- 1
Let S={x ∈ R; -π/2 < x < π/2 } and let V be the subset of R2 given by V=S^2={(x,y); -π/2 < x < π/2}, with vector addition ( (+) ).
For each (for every) u ∈ V, For each (for every) v ∈ V with u=(x1 , y1) and v=(x2,y2)
u+v = (arctan (tan(x1)+tan(x2)), arctan (tan(y1)+tan(y2)) )Note: The vectors are ordered pairs of real numbers between -π/2 and π/2, and we are using non-standard vector addition.
Show that V with the designated operations forms a vector space.
Make sure that you show verification for EACH of the ten Vector Space Axioms.
My question is how would you apply the additive identity to prove that u+0=u to show that V forms a vector space?
For each (for every) u ∈ V, For each (for every) v ∈ V with u=(x1 , y1) and v=(x2,y2)
u+v = (arctan (tan(x1)+tan(x2)), arctan (tan(y1)+tan(y2)) )Note: The vectors are ordered pairs of real numbers between -π/2 and π/2, and we are using non-standard vector addition.
Show that V with the designated operations forms a vector space.
Make sure that you show verification for EACH of the ten Vector Space Axioms.
My question is how would you apply the additive identity to prove that u+0=u to show that V forms a vector space?