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Homework Statement
Let V = {RXR} with addition defined as (a1,a2) + (b1,b2) = (a1 + b1, a2b2)
Show the vector space condition, for each x in V there exists a y in V such that x + y = 0, fails for the V defined above.
Homework Equations
The Attempt at a Solution
a + d = (a1,a2) + (d1,d2) = (a1 + d1, a2d2), so let d1 = -a1 and d2 = 0, therefore (a1 - a1, 0*a2) = (0,0) = 0
Seems to me that the condition holds. What have I missed?