Consider the group of nonzero real numbers, R* = R \ {0}, under mul- tiplication and the group of positive real numbers, R+, under multiplication. Let N = {1, -1}. Show that R*/N is isomorphic to R+ using the first isomorphism the- orem verifying each step. (Hint: Consider the function : R* → R+ be defined by |_ y(x) = |x|.)

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2Please help me to answer the question below.

Show that the function is a linear transformation. Is it also an isomorphism? Upload your proofs below. Let V be the space of infinite sequences of real numbers. T(x0, x1, x2, x3, x4..) = (x0, x2, x4, ...) from V to V (we are dropping every other term) OLinear but not an isomorphism OLinear and an isomorphism ONot Linear Choose File No file chosen