On R, define the operation of addition by (x, y) (x2, y2) = (x1x2, Y1Y2). Do...

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On R², define the operation of addition by (x₁, y₁) (x2, y2) = (x1x2, Y1Y2). Do axioms (A5) and (A6) in the definition of a vector space hold? Justify your answer. On R², define the operation of addition by (x₁, y₁) (x2, y2) = (x1x2, Y1Y2). Do axioms (A5) and (A6) in the definition of a vector space hold? Justify your answer.

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To determine if axioms A5 and A6 hold for the operation of addition on R defined as x1 y1 x y x1x yy2 we need to examine the properties of vector addition in a vector space A5 Closure under Addition For axiom A5 to hold the sum of two vectors in R using the defined addition operation must result in another vector in R Lets consider two arbitrary vectors x1 y1 and x2 y2 in R when we add them using the defined addition operation we get x1 y x y x1x yy ... View the full answer