can you please provide explanantions (1) Let T : R¹ → R² be given by T((x, y, w, z)) = (x+y, w z) for any (x, y, w, z) € R¹.Prove that I is a linear mapping, by checking the two defining properties hold.Compute the nullity and the rank of T.Determine, justifying your answer, whether T is injective, surjective and/or anisomorphism.

Answered: Image /qna-images/answer/0f41ccb5-e2e0-4e63-bcb6-9918a83b321f.jpg

Answered: 1) Let T R¹ R2 be given by T((x, y, w,…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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1) Let T R¹ R2 be given by T((x, y, w, z)) = (x+y, w-z) for any (x, y, w, z) = R¹. Prove that I is a linear mapping, by checking the two defining properties hold. Compute the nullity and the rank of T. Determine, justifying your answer, whether T is injective, surjective and/or an isomorphism.