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Let V = R2. Suppose in V vector addition is defined by x+y=(α1x1 +β1y1,α2x2 +β2y2)

for all x = (x1, x2), y = (y1, y2) ∈ V , α1, α2, β1, β2 some fixed real numbers, and scalar multiplication is the usual scalar multiplication. What values of α1 , α2 , β1 , β2 make V a vector space (over R).

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