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The set R^2 with addition and scalar multiplication defined by (x1, y1) + (x2, y2) = (x1...

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Basic Math

The set R^2 with addition and scalar multiplication definedby

(x1, y1) + (x2, y2) = (x1 + x2, y1 + y2)

c(x1, y1) = (cx1, y1)

is not a vector space. Determine which axiom fails and find acounterexample that shows that it fails.

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