Question

Suppose that V is a vector space, and u, v, w belongs to V. If w + u = w + v, then prove that

u= v.​

Answer 1

Given:

• u , v , w belongs to V
• w + u = w + v

To Prove :

• Prove that u = v

Solution :

${\small{\tt{w + u = w + v}}}$

${\small{\tt{\implies{u = w + v - w}}}}$

${\small{\tt{\implies{u = v}}}}$

Hence , Proved

Answer 2

Answer:

we have to prove

u=v.

so, w+u=w+v

u= v+w-w

-w+w will cancelled

u=v

hence Proved