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Let V be the set of vectors [2x − 3y, x + 2y, −y, 4x] with...

Let V be the set of vectors [2x − 3y, x + 2y, −y, 4x] with x, y R2. Addition and scalar multiplication are defined in the same way as on vectors. Prove that V is a vector space. Also, point out a basis of it.

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