4. Let V = {(x, y) | x, y ER}. Consider the operations "addition" and "scalar multipli-cation" defined by:VxV→V, ((x₁, y₁), (T2, Y2)) → (T₁, Y₁) + (x2, Y₂) = (x₁ + x₂ +1, Y₁+₂)RxV→V, (c, (x₁, y₁)) →co (x₁, y₁) = (cr₁+c-1, cy₁).Prove that V with these operations is a vector space over R.

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Answered: 1. Let V = {(x, y) | x,y ER}. Consider…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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1. Let V = {(x, y) | x,y ER}. Consider the operations "addition" and "scalar multipli- cation" defined by: VxV→V, ((₁, ₁), (2, 2)) → (11.₁) (2, 2) = (₁ +2₂+1, 31 +92) RXV V, (c, (x, y))→co (r₁, y) = (cri+c-1, cy₁). Prove that V with these operations is a vector space over R.