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Consider the set V = (x,y) x,y ∈ R with the following two operations: • Addition:...

Consider the set V = (x,y) x,y ∈ R with the following two operations: • Addition: (x1,y1)+(x2,y2)=(x1 +x2 +1, y1 +y2 +1) • Scalarmultiplication:a(x,y)=(ax+a−1, ay+a−1). Prove or disprove: With these operations, V is a vector space over R

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