Recent content by babygotpi

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    Abstract Algebra Proof Using the First Isomorphism Theory

    I don't understand. Did I not show it was onto?
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    Abstract Algebra Proof Using the First Isomorphism Theory

    Thanks. Glad to be part of PF. This is my final answer. Define mapping f: ℝ2 -> ℝ as follows: f(x,y) = 3x - 4y Claim: f is a homomorphism Pick any X, X1 ∈ ℝ2 in which X = (x1, y1) and x1 = (x2, y2). Then: f(x*x1 ) = f(x1+y1, x2+y2) = f(x1+y1) +f(x2 +y2) = f(x+x1 ). Hence, f...
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    Abstract Algebra Proof Using the First Isomorphism Theory

    Homework Statement See attatchment. I couldn't upload the picture. 2. The attempt at a solution I have the following: Define mapping f: ℝ2 -> ℝ as follows: f(x,y) = 3x - 4y Claim: f is a homomorphism Pick any (x,y) in ℝ2. Then f(x,y) = f(x)*f(y) = 3x - 4y = (x+x+x)-(y+y+y+y) =...