In: Advanced Math
Show that the set ℝ2R2, equipped with operations
(?1,?1)+˜(?2,?2)=(?1+?2+1,?1+?2−1)(x1,y1)+~(x2,y2)=(x1+x2+1,y1+y2−1)
? ⋅˜ (?,?)=(??+?−1,??−?+1)
(1)defines a vector space over ℝR.
(2)Show that the vector space ?V defined in question 1 is isomorphic to ℝ2R2 equipped with its usual vector space operations. This means you need to define an invertible linear map ?:?→ℝ2T:V→R2.