Determine whether the given sets with given operations are vector spaces? For those that are not...

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Determine whether the given sets with given operations are vector spaces? For those that are not vector spaces verify the vector space axiom they fail. a) The set of all ordered pairs of real numbers with the addition and scalar multiplication defined by (x1.V1) + (x,,Y2) = (x1 + x, + 1,y, + y, + 1) k(x, y)=(kx, ky) b) The set of all real numbers x such that x 20 with addition and scalar multiplication defined as x +y = xy +1 kx = k'x Determine whether the given sets with given operations are vector spaces? For those that are not vector spaces verify the vector space axiom they fail. a) The set of all ordered pairs of real numbers with the addition and scalar multiplication defined by (x1.V1) + (x,,Y2) = (x1 + x, + 1,y, + y, + 1) k(x, y)=(kx, ky) b) The set of all real numbers x such that x 20 with addition and scalar multiplication defined as x +y = xy +1 kx = k'x

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