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...

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.

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Expert Solution

Colby Messinger answered 1 year ago

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